Question

what is the volume of this cone?
round your answer to the nearest hundredth.
18 mm
9 mm
381.51
1,526.04
190.76
763.02
a cone has a height of 12 millimeters and a diameter of 22 millimeters.
what is its volume?
round your answer to the nearest hundredth.
1,519.76
379.94
759.88
3039.52

Explanation:

Step1: Recall the volume formula for a cone

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

Step2: Solve the first cone problem

For the first cone, the radius \( r = 9\space mm \) and the height \( h=18\space mm \).
Substitute into the formula:
\( V=\frac{1}{3}\times\pi\times(9)^{2}\times18 \)
First, calculate \( 9^{2}=81 \), then \( 81\times18 = 1458 \).
Then, \( \frac{1}{3}\times1458=486 \).
Now, \( V = 486\times\pi\approx486\times3.14159\approx1526.04 \) (rounded to the nearest hundredth).

Step3: Solve the second cone problem

For the second cone, the diameter \( d = 22\space mm \), so the radius \( r=\frac{d}{2}=\frac{22}{2} = 11\space mm \), and the height \( h = 12\space mm \).
Substitute into the formula:
\( V=\frac{1}{3}\times\pi\times(11)^{2}\times12 \)
First, calculate \( 11^{2}=121 \), then \( 121\times12 = 1452 \).
Then, \( \frac{1}{3}\times1452 = 484 \).
Now, \( V=484\times\pi\approx484\times3.14159\approx1519.76 \) (rounded to the nearest hundredth).

Answer:

First cone: 1,526.04
Second cone: 1,519.76