Question

jude says that the volume of a square pyramid with base edges of 7 in and a height of 7 in is equal to the volume of a cylinder with a radius of 7 in and a height of 7 in. jude rounded all answers to the nearest whole number. examine judes calculations. is he correct? volume of square pyramid volume of cylinder v = b(h) v = r²h v = 49(7) v = (7²)(7) v = 343 in³ v = 343 in³ yes, his calculations are correct and the volumes for figures are equal. no, he made a mistake in solving for the volume of the square pyramid. yes, but he made a mistake in solving for the volume of the cylinder. no, he made a mistake in solving for the volume of both figures.

Explanation:

Step1: Recall volume formulas

The volume formula for a square - pyramid is $V=\frac{1}{3}Bh$, where $B$ is the base area and for a square base with side length $s$, $B = s^{2}$, and the volume formula for a cylinder is $V=\pi r^{2}h$.

Step2: Calculate volume of square - pyramid

Given $s = 7$ in, so $B=s^{2}=7^{2}=49$ in² and $h = 7$ in. Then $V_{pyramid}=\frac{1}{3}\times49\times7=\frac{343}{3}\approx114$ in³.

Step3: Calculate volume of cylinder

Given $r = 7$ in and $h = 7$ in. Then $V_{cylinder}=\pi r^{2}h=\pi\times7^{2}\times7=343\pi\approx343\times 3.14 = 1077$ in³.

Step4: Analyze Jude's calculations

Jude used the wrong formula for the square - pyramid. He used $V = Bh$ instead of $V=\frac{1}{3}Bh$.

Answer:

No, he made a mistake in solving for the volume of the square pyramid.