Question

round your answer to the nearest hundredth
17 in
14 in
1743.75
435.94
6974.98
3,487.49
what is the volume of this cone?
round your answer to the nearest hundredth.
18 mm
9 mm
1,526.04
381.51
763.02
190.76

Explanation:

First Cone (Green, 17 in height, 14 in radius)

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.

Step2: Substitute Values

Here, \( r = 14 \) in and \( h = 17 \) in. Plug into the formula:
\( V = \frac{1}{3} \times \pi \times (14)^2 \times 17 \)
First, calculate \( 14^2 = 196 \). Then:
\( V = \frac{1}{3} \times \pi \times 196 \times 17 \)
\( 196 \times 17 = 3332 \), so \( V = \frac{1}{3} \times \pi \times 3332 \)
\( \frac{3332}{3} \approx 1110.6667 \), then multiply by \( \pi \approx 3.1416 \):
\( V \approx 1110.6667 \times 3.1416 \approx 3487.49 \) (rounded to nearest hundredth).

Second Cone (Purple, 18 mm height, 9 mm radius)

Step1: Recall Cone Volume Formula

\( V = \frac{1}{3}\pi r^2 h \), where \( r = 9 \) mm, \( h = 18 \) mm.

Step2: Substitute Values

\( V = \frac{1}{3} \times \pi \times (9)^2 \times 18 \)
Calculate \( 9^2 = 81 \). Then:
\( V = \frac{1}{3} \times \pi \times 81 \times 18 \)
\( 81 \times 18 = 1458 \), so \( V = \frac{1}{3} \times \pi \times 1458 \)
\( \frac{1458}{3} = 486 \), then multiply by \( \pi \approx 3.1416 \):
\( V \approx 486 \times 3.1416 \approx 1526.04 \) (rounded to nearest hundredth).

Answer:

s:

• Green Cone Volume: \( \boldsymbol{3,487.49} \) (corresponds to the option 3,487.49)
• Purple Cone Volume: \( \boldsymbol{1,526.04} \) (corresponds to the option 1,526.04)