Question

jude says that the volume of a square pyramid with base edges of 9.7 in and a height of 9 in is equal to the volume of a cylinder with a radius of 5.47 in and a height of 3 in. jude rounded his answers to the nearest whole number. examine judes calculations. is he correct? volume of square pyramid volume of cylinder v = 1/3 b(h) v = πr²h v = 1/3(94.09)(9) v = π(5.47²)(3) v = 1/3(846.81) v = π(29.9209)(3) v = 282 in³ v = π(89.7627) v = 282 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 cylinder. 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 both figures. question 9 the population density of lemonland is 15 lemon trees per acre. exactly 795 lemon trees grow in lemonland. how many acres are in lemonland?

Explanation:

Step1: Recall volume formulas

Volume of 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, $s = 9.7$ in, so $B=(9.7)^{2}=94.09$ in² and $h = 9$ in. Then $V_{pyramid}=\frac{1}{3}(94.09)(9)=282.27\approx282$ in³.

Step2: Recall cylinder volume formula

Volume of a cylinder is $V_{cylinder}=\pi r^{2}h$. Given $r = 5.47$ in and $h = 3$ in. Then $V_{cylinder}=\pi(5.47)^{2}(3)\approx\pi(29.9209)(3)\approx282.27\approx282$ in³.

Answer:

Yes, his calculations are correct and the volumes for figures are equal.