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

1 answer

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:

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

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

  2. 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.