Question

A cylindrical drain pipe is 3 inches across the top and about 9 inches high. How many cubic inches of water could it hold​ (Use 3.14 for pi as needed. Round to the nearest​ hundredth)?  
Question content area bottom
Part 1
A.
254.34 in3
B.
169.56 in3
C.
63.59 in3
D.
127.17 in3

Answer 1

To find the volume of a cylindrical drain pipe, we use the formula for the volume \( V \) of a cylinder:

\[
V = \pi r^2 h
\]

where \( r \) is the radius and \( h \) is the height of the cylinder.

1. **Find the radius**: The diameter of the pipe is given as 3 inches, so the radius \( r \) is half of that:

\[
r = \frac{3}{2} = 1.5 \text{ inches}
\]

2. **Determine the height**: The height \( h \) of the cylinder is given as 9 inches.

3. **Substitute the values into the volume formula**:

\[
V = \pi (1.5)^2 (9)
\]

Calculating \( (1.5)^2 \):

\[
(1.5)^2 = 2.25
\]

Now substitute \( \pi \) with 3.14:

\[
V = 3.14 \times 2.25 \times 9
\]

Calculate \( 2.25 \times 9 \):

\[
2.25 \times 9 = 20.25
\]

Now calculate the volume:

\[
V = 3.14 \times 20.25
\]

Calculating \( 3.14 \times 20.25 \):

\[
3.14 \times 20.25 \approx 63.585
\]

Now we round to the nearest hundredth:

\[
V \approx 63.59 \text{ cubic inches}
\]

Thus, the answer is C. **63.59 in³**.