Question

round your answer to the nearest hundredth.
9 m
16 m
301.44
602.88
75.36
150.72
what is the volume of this cone ?
round your answer to the nearest hundredth.
17 mm
11 mm
1076.49
538.25
269.12
2152.99

Explanation:

First Cone (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: Use the cone volume formula

The volume of a cone is \( V = \frac{1}{3}\pi r^2 h \). Substitute \( r = 8 \), \( h = 9 \), and \( \pi \approx 3.14 \):
\( V = \frac{1}{3} \times 3.14 \times 8^2 \times 9 \)
\( V = \frac{1}{3} \times 3.14 \times 64 \times 9 \)
\( V = 3.14 \times 64 \times 3 \)
\( V = 3.14 \times 192 \)
\( V = 602.88 \)? Wait, no, wait: Wait, \( \frac{1}{3} \times 9 = 3 \), so \( 3.14 \times 64 \times 3 = 3.14 \times 192 = 602.88 \)? But wait, no, let's recalculate. Wait, \( 8^2 = 64 \), \( 64 \times 9 = 576 \), \( \frac{1}{3} \times 576 = 192 \), \( 192 \times 3.14 = 602.88 \)? But the options include 301.44. Wait, maybe I made a mistake. Wait, no, the first cone: diameter 16, so radius 8, height 9. Wait, maybe the height is 9, but let's check the options. Wait, the first question's options: 301.44, 602.88, 75.36, 150.72. Wait, maybe I mixed up radius and diameter. Wait, no, diameter is 16, so radius 8. Wait, \( V = \frac{1}{3}\pi r^2 h = \frac{1}{3} \times 3.14 \times 8^2 \times 9 \). Let's compute \( 8^2 = 64 \), \( 64 \times 9 = 576 \), \( 576 \times \frac{1}{3} = 192 \), \( 192 \times 3.14 = 602.88 \). But the first option is 301.44, which is half of that. Wait, maybe the height is 9, but maybe the diagram is a cone with diameter 16 and height 9, but maybe I misread the height. Wait, the first cone: the dotted line is height 9, diameter 16. Wait, maybe the answer is 602.88? But let's check the second cone.

Second Cone (radius 11 mm, height 17 mm)

Step1: Identify radius and height

Radius \( r = 11 \) mm, height \( h = 17 \) mm.

Step2: Use the cone volume formula

\( V = \frac{1}{3}\pi r^2 h \). Substitute \( r = 11 \), \( h = 17 \), \( \pi \approx 3.14 \):
\( V = \frac{1}{3} \times 3.14 \times 11^2 \times 17 \)
\( V = \frac{1}{3} \times 3.14 \times 121 \times 17 \)
\( V = \frac{1}{3} \times 3.14 \times 2057 \)
\( V = \frac{6458.98}{3} \approx 2152.99 \)? But the options include 2152.99. Wait, the second cone's options: 1076.49, 538.25, 269.12, 2152.99. So 2152.99 is an option. But let's go back to the first cone. Wait, maybe I made a mistake in the first cone. Wait, the first cone: diameter 16, so radius 8, height 9. Wait, maybe the height is 9, but the formula is \( \frac{1}{3}\pi r^2 h \). Let's recalculate: \( 8^2 = 64 \), \( 64 \times 9 = 576 \), \( 576 \times \frac{1}{3} = 192 \), \( 192 \times 3.14 = 602.88 \). But the first option is 301.44, which is half of that. Wait, maybe the height is 4.5? No, the diagram shows 9 m. Wait, maybe the first cone's height is 9, but the options have 301.44. Wait, 301.44 is \( \frac{1}{3} \times 3.14 \times 8^2 \times 4.5 \). Wait, maybe I misread the height. Wait, the first cone: the dotted line is 9 m, but maybe it's the slant height? No, the dotted line is the height (perpendicular to the base). Wait, if it's the slant height, then we need to find the height. Wait, slant height \( l = 9 \), diameter 16, so radius 8. Then height \( h = \sqrt{l^2 - r^2} = \sqrt{81 - 64} = \sqrt{17} \approx 4.12 \), which doesn't match. So probably the first cone's height is 9, radius 8. Then volume is 602.88, but that's an option. Wait, the first cone's options: 301.44, 602.88, 75.36, 150.72. So 602.88 is an option. But let's check the second cone. The second cone: radius 11, height 17. Volume is \( \frac{1}{3} \times 3.14 \times 11^2 \times 17 = \frac{1}{3} \times 3.14 \times 121 \times 17 = \frac{1}{3} \times 3.14 \times 2057 = \frac{6458.98}{3} \approx 2152.99 \), which is an option.

But let's focus on the first cone. Wait, maybe I made a mistake. Wait, the first cone: diameter 16, so radius 8, height 9. Volume: \( \frac{1}{3} \times 3.14 \times 8^2 \times 9 = \frac{1}{3} \times 3.14 \times 64 \times 9 = 3.14 \times 64 \times 3 = 3.14 \times 192 = 602.88 \). So the answer for the first cone is 602.88.

For the second cone: radius 11, height 17. Volume: \( \frac{1}{3} \times 3.14 \times 11^2 \times 17 = \frac{1}{3} \times 3.14 \times 121 \times 17 = \frac{6458.98}{3} \approx 2152.99 \), which is the last option.

But let's confirm the first cone again. Wait, the first cone's options: 301.44, 602.88, 75.36, 150.72. If we take \( \pi = 3.14 \), radius 8, height 9: \( \frac{1}{3} \times 3.14 \times 64 \times 9 = 602.88 \). So that's correct.

Answer:

(First Cone):
602.88