Match Formula To Problem

To solve problems involving area, surface area, or volume, it is crucial to identify the appropriate formula that corresponds to the problem. Once the formula is identified, it is important to accurately copy the formula and substitute the correct numbers into it. Finally, it is necessary to double-check the calculations to ensure that addition, multiplication, or division has been done accurately. This statement emphasizes the importance of these steps in successfully solving problems related to area, surface area, or volume.

The explanation for the given correct answer is that looking for key words in problems and selecting the correct formula before solving area, volume, and surface area problems is indeed important. This approach helps in identifying the relevant information and applying the appropriate mathematical concepts to solve the problems accurately. By doing so, one can ensure that the calculations are done correctly and the solutions are obtained efficiently.

To find the area of a parallelogram, you multiply the base by the height. In this case, the base is 15 m and the height is 12 m. Therefore, the area of the parallelogram is 15 multiplied by 12, which equals 180 square meters.

To find the area of a triangle, we use the formula: Area = (base x height) / 2. In this case, the base is 20 and the height is 4. So, the area of the triangle would be (20 x 4) / 2.

When trying to determine the inside capacity of a box, you are measuring its volume. Volume refers to the amount of space occupied by an object or contained within a container. In the context of a box, volume represents the amount of space available inside the box to hold objects. Perimeter, area, and surface area are measurements that pertain to the outer boundaries or surfaces of an object, rather than its internal capacity.

To find the area of a trapezoid, you can use the formula A = (b1 + b2) * h / 2, where b1 and b2 are the lengths of the bases and h is the height. In this case, the formula is correctly applied as A = (12 + 8) * 10 / 2, which simplifies to 20 * 10 / 2. This gives us an area of 100 square inches.

When you want to obtain the total area of every face of a solid figure, you are trying to find the surface area of that solid. Surface area refers to the sum of the areas of all the faces of a three-dimensional object. It is used to measure the amount of material needed to cover the surface of the object. In contrast, volume refers to the amount of space occupied by the object, while area typically refers to the measure of the size of a two-dimensional shape.

The correct way to set up the problem is to multiply the length, width, and height together to find the volume of the rectangular prism. In this case, the volume is found by multiplying 9 ft (length) by 4 ft (width) by 21 ft (height).

To determine how much wallpaper is needed to cover one wall of a room, you should calculate the area of that wall. The area represents the total surface of the wall that needs to be covered with wallpaper. Perimeter refers to the distance around the wall, while volume is the measure of the space inside the wall. Therefore, the correct answer is area, as it directly relates to the amount of wallpaper required for coverage.

The formula for finding the surface area of a rectangular prism is 2lw + 2lh + 2wh. In this case, the length is 4 inches, the width is 6 inches, and the height is 3 inches. Plugging these values into the formula, we get 2 x 3 x 4 + 2 x 3 x 6 + 2 x 4 x 6, which simplifies to 24 + 36 + 48, or 108. Therefore, the surface area of the rectangular prism is 108 square inches.