Question

jude says that the volume of a square pyramid with base edges of 12 in and a height of 10 in is equal to the volume of a cylinder with a radius of 6.77 in and a height of 10 in. jude rounded his answers to the nearest whole numbers. examine judes calculations. is he correct? volume of square pyramid: v = 1/3(b)(h), v = 1/3(144)(10), v = 1/3(1440), v = 480 in³. volume of cylinder: v = 1/3πr²h, v = 1/3π(6.77²)(10), v = 1/3π(45.8329)(10), v = 1/3π(458.329), v ≈ 480 in³. no, he made a mistake in solving for the volume of both figures. yes, but he made a mistake in solving for the volume of the square pyramid. no, he made a mistake in solving for the volume of the cylinder. yes, his calculations are correct and the volumes for figures are equal.

Explanation:

Step1: Recall volume formulas

The volume formula for a square - pyramid is $V_{pyramid}=\frac{1}{3}Bh$, where $B$ is the base area. For a square base with side length $s$, $B = s^{2}$. Here, $s = 12$ in, so $B=12^{2}=144$ in² and $h = 10$ in. Then $V_{pyramid}=\frac{1}{3}(144)(10)=480$ in³.

Step2: Recall cylinder volume formula

The volume formula for a cylinder is $V_{cylinder}=\pi r^{2}h$. Here, $r = 6.77$ in and $h = 10$ in. So $V_{cylinder}=\pi(6.77)^{2}(10)\approx\pi(45.8329)(10)\approx 458.329\pi\approx1440$ in³ (rounded to the nearest whole number).

Since $480
eq1440$, Jude made a mistake.

Answer:

No, he made a mistake in solving for the volumes of both figures.