Question

a cone has a height of 8 centimeters and a diameter of 8 centimeters. what * 1 point is its volume?
round your answer to the nearest hundredth.
○ 66.98
○ 33.49
○ 133.97
○ 267.94

a cone has a height of 18 centimeters and a radius of 7 centimeters. what * 1 point is its volume?
round your answer to the nearest hundredth.
○ 461.58
○ 230.79
○ 923.16
○ 1846.32

Explanation:

First Cone Volume Problem

Step1: Recall cone volume formula

The volume \( V \) of a cone is given by \( V = \frac{1}{3}\pi r^2 h \), where \( r \) is the radius and \( h \) is the height. Given diameter \( d = 8 \) cm, radius \( r=\frac{d}{2}=\frac{8}{2} = 4 \) cm, height \( h = 8 \) cm.

Step2: Substitute values into formula

Substitute \( r = 4 \), \( h = 8 \) into \( V=\frac{1}{3}\pi r^2 h \):
\( V=\frac{1}{3}\times\pi\times4^2\times8=\frac{1}{3}\times\pi\times16\times8=\frac{128\pi}{3}\approx\frac{128\times3.1416}{3}\approx133.97 \) (rounded to nearest hundredth).

Step1: Recall cone volume formula

The volume \( V \) of a cone is \( V=\frac{1}{3}\pi r^2 h \), with \( r = 7 \) cm, \( h = 18 \) cm.

Step2: Substitute values into formula

Substitute \( r = 7 \), \( h = 18 \) into \( V=\frac{1}{3}\pi r^2 h \):
\( V=\frac{1}{3}\times\pi\times7^2\times18=\frac{1}{3}\times\pi\times49\times18 = 294\pi\approx294\times3.1416\approx923.16 \) (rounded to nearest hundredth).

Answer:

133.97 (corresponding option: 133.97)

Second Cone Volume Problem