Chapter 12: Solids

A sliced potato cooks faster in boiling oil because the increased surface area allows for more heat transfer. The oil can penetrate and cook the slices more evenly and quickly compared to a whole potato, which has a larger volume and takes longer to heat through.

A kilogram of peaches has more skin area than a kilogram of grapefruits. This is because the surface area of the fruit is directly proportional to its size. Since grapefruits are larger than peaches, a kilogram of grapefruits would have a larger overall surface area, including the skin. Therefore, the correct answer is grapefruits.

The density of an object is calculated by dividing its mass by its volume. In this case, the mass of the wooden block is given as 1000 kg and the volume is given as 2 cubic meters. By dividing the mass by the volume, we get a density of 500 kg per cubic meter.

Elephants have more skin compared to mice. This is because elephants are much larger in size and have a greater surface area to cover. Their skin is also thicker and more wrinkled, allowing them to withstand the harsh environmental conditions they live in. In contrast, mice have relatively smaller bodies and less skin. Therefore, the correct answer is elephant.

When the iron block is heated, its particles gain energy and move faster, causing the block to expand. As the volume of the block increases while the mass remains the same, the density decreases. This is because density is defined as mass divided by volume, and when the volume increases, the density decreases. Therefore, in the expanded condition, the density of the iron block is less.

The volume of an object can be calculated by dividing its mass by its density. In this case, the mass of the metal block is given as 15,000 kg and the density is given as 5000 kg per cubic meter. By dividing the mass by the density, we get 15,000 kg / 5000 kg per cubic meter = 3 cubic meters. Therefore, the volume of the metal block is 3 cubic meters.

If the mass of an object were to double while its volume remains the same, its density would double. Density is defined as mass divided by volume. If the mass doubles while the volume remains the same, the ratio of mass to volume (density) would also double.

When weight is applied to the top of a stone arch, the stone blocks in the arch experience compression. Compression is a force that pushes or squeezes an object, causing it to become smaller or more compact. In the case of a stone arch, the weight from the top pushes down on the stones, causing them to be compressed and tightly packed together. This compression helps to distribute the weight evenly across the arch and allows it to support the load without collapsing.

When the weight of the block is distributed equally between the two springs, each spring only needs to support half of the weight. Since the weight is directly proportional to the amount of stretch in the spring, each spring will only stretch half as much as it did when it was supporting the entire weight of the block. Therefore, each spring will stretch 5 cm.

When a chocolate bar is cut in half, its density remains unchanged. Density is defined as the mass of an object divided by its volume. Cutting a chocolate bar in half does not change the mass or the volume of the bar. Therefore, the ratio of mass to volume, which is the definition of density, remains the same.

Both the lake full of water and the cup full of lake water have the same density. Density is a property of a substance and is defined as the mass of a substance per unit volume. Since both the lake water and the cup of lake water are made up of the same substance (water), they will have the same density. The size of the lake or the cup does not affect the density of the water.

If you make cupcakes and bake them as directed for a cake, you will find the cupcakes overbaked. This is because cupcakes are smaller and require less baking time compared to cakes. Baking them for the same duration as a cake will result in overbaking, causing them to become dry and possibly burnt.

The strength of a rope depends on its thickness. A thicker rope has more material, which allows it to withstand greater tension and weight without breaking. The thickness of a rope directly affects its ability to bear load and resist stretching or snapping under pressure. Therefore, the thickness of a rope is a crucial factor in determining its strength. Length, on the other hand, does not directly impact the strength of a rope but may affect its overall functionality and usefulness in certain situations.

A pure gold ring has the same density as a bar of pure gold because both are made of the same material, which is gold. Density is a measure of how much mass is packed into a given volume, and since both the ring and the bar are made of the same substance, they will have the same density.

A sphere has the least surface area for a given volume compared to other geometrical shapes. This is because a sphere has a symmetrical shape, allowing it to enclose the maximum volume with the least amount of surface area. The surface area of a sphere is given by the formula 4πr^2, where r is the radius of the sphere. Since the radius is squared in the formula, increasing the radius will increase the volume at a faster rate compared to the surface area. Therefore, a sphere has the smallest surface area for a given volume.

A larger turkey takes more time per pound to cook compared to a medium-sized turkey. This is because the larger turkey has more mass and therefore requires more time for the heat to penetrate and cook the meat thoroughly. The additional time is needed to ensure that the center of the turkey reaches the desired internal temperature, while still maintaining the outer layers from becoming overcooked or dry.

The density of a substance is defined as its mass per unit volume. In this case, the density of the metal block is given as 5000 kg per cubic meter. The volume of the block is given as 2 cubic meters. To find the mass of the block, we can use the formula: mass = density * volume. Substituting the given values, we get mass = 5000 kg/m^3 * 2 m^3 = 10,000 kg. Therefore, the correct answer is 10,000 kg.

When a 100-N weight is suspended from the unstretched hanging spring, the spring elongates by 10 cm (60 cm - 50 cm). This means that the spring constant, which represents the stiffness of the spring, is 10 N/cm. Adding another 100-N weight will double the force acting on the spring, causing it to elongate by another 10 cm. Therefore, the spring's length will be 70 cm (60 cm + 10 cm).

When a load is placed on the middle of a horizontal beam supported at each end, the bottom part of the beam undergoes tension. This is because the load causes the top part of the beam to experience compression, which in turn creates tension in the bottom part of the beam to maintain balance.

A mouse has more skin compared to its body weight than an elephant. This is because mice have a higher surface area-to-volume ratio, meaning they have a larger amount of skin relative to their body size.

Small potatoes are likely to produce more peelings compared to large potatoes because they have a higher surface area to volume ratio. Since the peelings are obtained by peeling the outer layer of the potatoes, the smaller potatoes with their smaller size would have more surface area in proportion to their volume, resulting in more peelings.

When the volume of an object doubles while its mass stays the same, the density is calculated by dividing the mass by the volume. Since the mass remains constant, while the volume doubles, the resulting density will be half of the original value. Therefore, the correct answer is "halve."

The correct answer is "its radiating area is small compared to its volume." This means that despite its large size, an elephant has a relatively smaller surface area through which it can lose heat compared to its overall body volume. This is advantageous in hot environments as it helps the elephant retain more heat and conserve energy.

When a spherical meatball is flattened into a hamburger, its shape changes from a three-dimensional sphere to a two-dimensional circle. This change in shape increases the surface area of the meatball, as the flat hamburger now has more exposed surface compared to the spherical meatball. The volume, on the other hand, remains the same as it is determined by the amount of meat used, which does not change when the meatball is flattened. Therefore, the correct answer is surface area.

When a strong spring is stretched by a weight, the amount of stretch is directly proportional to the weight applied. In this case, when the weight is doubled, the spring will stretch another 10 cm, making the total stretch 20 cm. This is because the weight is directly proportional to the amount of stretch in the spring.

When a loaf of bread is compressed, its density increases. Compression reduces the volume of the bread while keeping the mass constant, resulting in a higher concentration of molecules within a smaller space. This leads to an increase in density, as the same amount of mass is now packed into a smaller volume. The other options, such as surface tension becoming less or molecules becoming harder, do not accurately describe the effect of compression on the bread.

If all sized potatoes are selling at the same price per kilogram, buying large potatoes will give you more potato for your money when you peel them for mashing. This is because larger potatoes will have a higher weight and volume, so when you peel them, you will still have a significant amount of potato left compared to smaller potatoes. Therefore, buying large potatoes would be more cost-effective in this scenario.

When each dimension of a steel bridge is scaled up ten times, its strength is multiplied by the cross-sectional area, which is proportional to the square of the scaling factor (10^2 = 100). Therefore, the strength of the bridge is multiplied by 100. However, the weight of the bridge is proportional to the volume, which is proportional to the cube of the scaling factor (10^3 = 1000). Thus, the weight of the bridge is multiplied by 1000.

When two identical springs are used in series, the effective spring constant is halved, while the effective length is doubled. In this case, the original spring is stretched 10 cm by the 1-kg block. When the two springs are used together, the effective length becomes 20 cm (10 cm x 2) and the effective spring constant is halved. Therefore, the total stretch of the double-length spring will be 20 cm.

When the linear size of an object is doubled, its area is multiplied by 2 because area is a two-dimensional measurement and doubling the length and width results in a four times larger area. Similarly, the volume of the object is multiplied by 8 because volume is a three-dimensional measurement and doubling the length, width, and height results in an eight times larger volume. Therefore, the correct answer is that doubling the linear size of an object multiplies its area by 2 and its volume by 8.

When the linear size of an object is tripled, its area is multiplied by 3 because the area of a two-dimensional object is proportional to the square of its linear size. Similarly, the volume of a three-dimensional object is proportional to the cube of its linear size. Therefore, when the linear size is tripled, the volume is multiplied by 3^3, which is 27. Hence, the correct answer is that tripling the linear size of an object multiplies its area by 3 and its volume by 27.

If the candymaker buys 100 kg of small apples instead of 100 kg of large apples, she will need more taffy. This is because small apples have a larger surface area compared to large apples, which means that more taffy will be needed to cover each small apple. Therefore, choosing small apples would require an increased amount of taffy.

The density of a substance is defined as its mass per unit volume. In this case, we are comparing the density of a kilogram of feathers to the density of a kilogram of lead. Since lead is a much denser material compared to feathers, a kilogram of lead would occupy less volume than a kilogram of feathers. Therefore, the density of a kilogram of lead is more than the density of a kilogram of feathers.

Mittens are a better choice in cold weather because they keep your fingers together, allowing them to generate and retain more heat. Gloves, on the other hand, separate your fingers, which can result in more heat loss. Therefore, wearing mittens will provide better insulation and keep your hands warmer compared to gloves.

If object A in your left hand and object B in your right hand both have the same weight density, it means that the weight of each object is distributed equally per unit volume. This implies that the mass of each object is also distributed equally per unit volume, resulting in equal mass densities. Therefore, the correct answer is that the objects have equal mass densities.

Stone slabs are stronger under compression because they are able to withstand and distribute the force evenly across their structure. When subjected to compression, the stone slabs are able to resist the crushing or collapsing forces, making them more resistant to damage. On the other hand, tension forces can cause the stone slabs to break or crack, as they are not as effective in resisting pulling or stretching forces. Therefore, stone slabs are generally considered to be stronger under compression rather than tension.

When eight little spheres of mercury coalesce to form a single sphere, the surface area of the big sphere will be less than the combined surface areas of the eight little spheres. This is because when the little spheres combine, there is a reduction in the total surface area due to the merging of the individual surfaces. The surface area of a sphere is directly proportional to its volume, and since the volume of the big sphere is the same as the combined volumes of the little spheres, the surface area will be less.

Drilling the bolt-holes through the web of the I-beam will weaken the beam the least. The web is the vertical section of the I-beam that connects the upper and lower flanges. By drilling the bolt-holes through the web, the structural integrity of the flanges, which bear most of the load, remains intact. This ensures that the beam retains its strength and stability, minimizing any weakening effects caused by the bolt-holes.

When small creatures fall from great heights, the effects of scaling can be beneficial to them. Scaling refers to the relationship between an object's size and its physical properties. In this case, small creatures have a higher surface area to volume ratio, which means they experience more air resistance when falling. This increased air resistance helps slow down their descent and reduces the impact force when they hit the ground, minimizing the risk of injury. Therefore, the effects of scaling are beneficial to small creatures that fall from great heights.

If an elephant grew to twice its height, the area of its ears would be about four times what it was. This is because the area of a two-dimensional shape, such as the ears, is directly proportional to the square of its dimensions. If the height of the elephant doubles, the dimensions of its ears would also double, resulting in an area that is four times larger than before.

Swimmers who are relatively large can benefit from the effects of scaling. Scaling refers to the concept of adjusting body size or proportions to optimize performance. In swimming, larger swimmers tend to have a longer reach, more surface area, and increased buoyancy, which can give them an advantage in the water. These factors allow them to generate more power and maintain better body position, resulting in improved speed and efficiency. Therefore, the effects of scaling are beneficial for swimmers who are relatively large.

If the incredible shrinking man shrinks proportionately to 1/10 his original height, his weight will be multiplied by 0.001. This is because when an object's size decreases by a factor of 1/10, its volume (and therefore weight) decreases by a factor of (1/10)^3, which is equal to 0.001. Therefore, the correct answer is 0.001.

When a living cell doubles in diameter, the amount of its material to be nourished is multiplied by eight because the volume of a sphere is proportional to the cube of its radius. However, the amount of membrane through which to feed it is only multiplied by four because the surface area of a sphere is proportional to the square of its radius. Therefore, the correct answer is 4.

When the length and diameter of a pencil are both multiplied by 10, the volume of the pencil will be multiplied by 10^3, which is 1000. This is because the volume of a cylinder is calculated by multiplying the area of the base (which is proportional to the square of the diameter) by the height (which is proportional to the length). By multiplying both the diameter and length by 10, we are effectively multiplying the volume by 10^2, resulting in a multiplication factor of 1000.

The density of a substance is calculated by dividing its mass by its volume. In this case, the metal block has a mass of 5 grams and a volume of 1 cubic centimeter, giving it a density of 5 grams per cubic centimeter (5 g/cc). Since the piece of metal being compared has the same kind of metal, its density would also be 5 g/cc, as the density of a substance remains constant regardless of its volume.

The density of lead is much higher than the density of feathers. This means that a kilogram of lead takes up much less space than a kilogram of feathers. Therefore, the volume of a kilogram of lead is less than the volume of a kilogram of feathers.

If an elephant grows to twice its normal height, it will have a larger volume and therefore a larger weight. The weight of an object is directly proportional to its volume. Since the height is doubled, the volume will be multiplied by 2^3 = 8. Therefore, the weight will also be multiplied by 8.

When the eight little spheres coalesce to form a single sphere, their surfaces combine to create the surface of the big sphere. Since each little sphere has the same surface area, the total surface area of the big sphere is equal to the sum of the surface areas of the eight little spheres. Since the big sphere is formed by combining eight equal-sized spheres, its surface area is double the surface area of one of the little spheres. Therefore, the correct answer is one half.

Doubling the thickness (diameter) of a rope will multiply its strength by 4. This is because the strength of a rope is directly proportional to its cross-sectional area, which is determined by the square of its diameter. Therefore, if the diameter is doubled, the cross-sectional area is quadrupled, resulting in a fourfold increase in strength.

A dome-shaped house is more heat efficient than a rectangular house because it has less area compared to its volume. This means that there is less surface area for heat to escape from, resulting in better insulation and heat retention. The compact shape of the dome reduces the amount of exposed surface area, minimizing heat loss and making it more energy-efficient.