For a project on Egypt, Nick is building a paper model of a square based pyramid. The square base measures 8 inches by 8 inches. The height is 9.2 inches. If Nick carves a piece of foam to place inside the pyramid for support, which measurement BEST describes the amount of foam used? (round to nearest whole number)
Responses
A 196 in2
196 in 2
B 196 in3
196 in 3
C 224 in3
224 in 3
D 224 in2
The correct answer is B.
To find the volume of the foam needed to support the pyramid, we can use the formula for the volume of a pyramid:
V = (1/3) * base area * height
The base area is the area of the square base, which is 8 inches by 8 inches:
base area = 8 in * 8 in = 64 in^2
Plugging in the given height of 9.2 inches:
V = (1/3) * 64 in^2 * 9.2 in ≈ 196 in^3
Therefore, Nick would need approximately 196 cubic inches of foam to support his paper pyramid.
To calculate the amount of foam used, we need to find the volume of the pyramid. The formula to calculate the volume of a pyramid is:
Volume = (Base Area * Height) / 3
Given that the square base measures 8 inches by 8 inches, the base area will be:
Base Area = 8 inches * 8 inches = 64 square inches
Now we can calculate the volume:
Volume = (64 square inches * 9.2 inches) / 3
Simplifying this equation gives us:
Volume ≈ 197.8666667 cubic inches
Rounding this to the nearest whole number gives us:
Volume ≈ 198 cubic inches
Therefore, the correct answer is A) 196 in3.