Question

Find the volume of a pyramid with a square base, where the perimeter of the base is

11.8 m and the height of the pyramid is 11.7 m. Round your answer to the nearest tenth of a cubic meter.
a) 145.8 m³
b) 151.5 m³
c) 162.4 m³
d) 169.1 m³

Answer 1

The volume of a pyramid with a square base, where the perimeter is 11.8 m, and the height is 11.7 m, is 33.8 m³ when rounded to the nearest tenth.

Step-by-step explanation:

First, we need to calculate the side length of the square base of the pyramid. Since the perimeter is 11.8 m, and a square has four equal sides, each side of the square is 11.8 m ÷ 4 = 2.95 m. The area of the square base is therefore 2.95 m × 2.95 m = 8.7025 m².

The volume of a pyramid is calculated using the formula V = (1/3) × base area × height. Plugging in our numbers: V = (1/3) × 8.7025 m² × 11.7 m = 33.8235 m³. Rounded to the nearest tenth, the volume is 33.8 m³.

Note that none of the answer choices provided match the correct calculation; thus, there may have been a mistake in the provided choices or in the understanding of the question.