Question

what is the volume of this cone?
round your answer to the nearest hundredth.
image of a cone with height 9 m and diameter 16 m
options: 150.72, 301.44, 602.88, 75.36

a cone has a height of 8 centimeters and a diameter of 8 centimeters. what is its volume?
round your answer to the nearest hundredth.
options: 66.98, 267.94, 33.49, 133.97

Explanation:

First Cone Problem (16 m diameter, 9 m height)

Step1: Find the radius

The diameter is 16 m, so the radius \( r=\frac{16}{2} = 8 \) m.

Step2: Recall the volume formula for a cone

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. Here, \( r = 8 \) m and \( h=9 \) m.

Step3: Substitute the values into the formula

\( V=\frac{1}{3}\times\pi\times8^{2}\times9 \)
First, calculate \( 8^{2}=64 \). Then, \( \frac{1}{3}\times9 = 3 \). So the formula becomes \( V=\pi\times64\times3=192\pi \).
Using \( \pi\approx3.14 \), \( V\approx192\times3.14 = 602.88 \) cubic meters.

Step1: Find the radius

The diameter is 8 cm, so the radius \( r = \frac{8}{2}=4 \) cm.

Step2: Use the cone volume formula

The volume \( V=\frac{1}{3}\pi r^{2}h \), with \( r = 4 \) cm and \( h = 8 \) cm.

Step3: Substitute the values

\( V=\frac{1}{3}\times\pi\times4^{2}\times8 \)
Calculate \( 4^{2}=16 \). Then, \( \frac{1}{3}\times8=\frac{8}{3} \). So \( V=\pi\times16\times\frac{8}{3}=\frac{128\pi}{3} \).
Using \( \pi\approx3.14 \), \( V\approx\frac{128\times3.14}{3}=\frac{401.92}{3}\approx133.97 \) cubic centimeters.

Answer:

602.88 (corresponding to the option with 602.88)

Second Cone Problem (8 cm diameter, 8 cm height)