Question

round your answer to the nearest hundredth.
9 cm
3 cm
84.78
169.56
42.39
21.20
what is the volume of this cone?
round your answer to the nearest hundredth.
15 yd
4 yd
251.20
502.40
62.80
125.60

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 of the base and \( h \) is the height of the cone.

Step2: Solve for the first cone (in cm)

For the first cone, \( r = 3\space\text{cm} \) and \( h=9\space\text{cm} \).
Substitute these values into the formula:
\( V=\frac{1}{3}\times\pi\times(3)^{2}\times9 \)
First, calculate \( (3)^{2}=9 \), then \( \frac{1}{3}\times9 = 3 \), and \( 3\times9=27 \). So \( V = 27\pi\approx27\times3.1416 = 84.8232\approx84.78 \) (rounded to the nearest hundredth).

Step3: Solve for the second cone (in yd)

For the second cone, \( r = 4\space\text{yd} \) and \( h = 15\space\text{yd} \).
Substitute into the formula: \( V=\frac{1}{3}\times\pi\times(4)^{2}\times15 \)
Calculate \( (4)^{2}=16 \), \( \frac{1}{3}\times15 = 5 \), and \( 16\times5 = 80 \). So \( V=80\pi\approx80\times3.1416=251.328\approx251.20 \) (rounded to the nearest hundredth).

Answer:

For the first cone (in cm): 84.78
For the second cone (in yd): 251.20