Question

what is the volume of this cylinder?
round your answer to the nearest hundredth.
image of a purple cylinder with radius 15 cm and height 14 cm (partially visible)
options:
9,891.00
4945.50
14836.50
2472.75
image of a green cylinder with diameter 38 in (radius 19 in) and height 10 in
options:
11,335.40
22,670.80
7556.93
2518.97

Explanation:

Step1: Recall Cylinder Volume Formula

The volume \( V \) of a cylinder is given by \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

Step2: Solve for the First Cylinder (15 cm radius, 14 cm height)

• Radius \( r = 15 \) cm, Height \( h = 14 \) cm.
• Substitute into the formula: \( V = \pi \times 15^2 \times 14 \)
• Calculate \( 15^2 = 225 \), then \( 225 \times 14 = 3150 \)
• Multiply by \( \pi \) (using \( \pi \approx 3.14 \)): \( V \approx 3.14 \times 3150 = 9891 \)? Wait, no, wait—wait, maybe the height is 14? Wait, no, maybe I misread. Wait, the first cylinder: radius 15 cm, height 14 cm? Wait, no, maybe the height is 14? Wait, no, let's recalculate. Wait, \( 15^2 = 225 \), \( 225 \times 14 = 3150 \), \( 3150 \times 3.14 = 9891 \)? But the options have 4945.50. Wait, maybe the height is 7? Wait, no, the image shows "14 c"—maybe 14 cm? Wait, no, maybe the radius is 15, height is 7? Wait, no, let's check the options. Wait, 4945.50 is half of 9891. Oh! Wait, maybe the height is 7? Wait, no, maybe I made a mistake. Wait, let's check the second cylinder. Wait, the first cylinder: radius 15, height 14. Wait, \( \pi r^2 h = 3.14 \times 15^2 \times 14 = 3.14 \times 225 \times 14 = 3.14 \times 3150 = 9891 \). But the options have 4945.50, which is half of that. Wait, maybe the height is 7? Wait, maybe the height is 14/2? No, the image says "14 c"—maybe 14 cm. Wait, maybe the radius is 15, height is 7? Wait, no, let's check the second problem. Wait, the second cylinder: diameter 38 in, so radius 19 in, height 10 in. Volume would be \( \pi \times 19^2 \times 10 = 3.14 \times 361 \times 10 = 11335.4 \), which matches the first option for the second cylinder. Wait, maybe the first cylinder's height is 7? Wait, no, the first cylinder: radius 15, height 7. Then \( 15^2 \times 7 = 1575 \), \( 1575 \times 3.14 = 4945.5 \), which is one of the options (4945.50). Ah! So maybe the height is 7, not 14. Maybe the "14 c" is a typo or misread, and it's 7 cm. So let's correct:

For the first cylinder:

• Radius \( r = 15 \) cm, Height \( h = 7 \) cm (assuming a misread, since 4945.50 is \( 15^2 \times 7 \times 3.14 \))
• \( V = \pi \times 15^2 \times 7 = 3.14 \times 225 \times 7 = 3.14 \times 1575 = 4945.5 \)

For the second cylinder (diameter 38 in, so radius 19 in, height 10 in):

• \( V = \pi \times 19^2 \times 10 = 3.14 \times 361 \times 10 = 11335.4 \), which matches the first option (11,335.40)

Answer:

For the first cylinder (15 cm radius, height likely 7 cm): 4945.50
For the second cylinder (38 in diameter, 10 in height): 11,335.40