Question

question 14(multiple choice worth 4 points)
(06 01 mc)
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 in?
v = 343 in³
o yes, his calculations are correct and the volumes for figures are equal.
o no, he made a mistake in solving for the volume of the square pyramid.
o yes, but he made a mistake in solving for the volume of the cylinder.
o no, he made a mistake in solving for the volume of both figures.
question 15(multiple choice worth 4 points)
(06 04 lc)
if a rectangle was rotated about the y - axis, like the one shown below, what would be the resulting three - dimensional shape?

Explanation:

Step1: Calculate the volume of the square pyramid

The formula for the volume of a square pyramid is \(V = \frac{1}{3}Bh\), where \(B\) is the base area. The base is a square with side - length \(s = 7\) in, so \(B=s^{2}=7^{2}=49\) in², and \(h = 7\) in. Then \(V=\frac{1}{3}\times49\times7=\frac{343}{3}\approx114.33\) in³.

Step2: Calculate the volume of the cylinder

The formula for the volume of a cylinder is \(V=\pi r^{2}h\). Given \(r = 7\) in and \(h = 7\) in, \(V=\pi\times7^{2}\times7=343\pi\approx1077.57\) in³.

Since the calculated volumes \(\frac{343}{3}\) (pyramid) and \(343\pi\) (cylinder) are not equal, Jude made a mistake in solving for the volume of the square pyramid.

Answer:

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