Question

The volume of a right circular cylinder is 29,673 inches3
. Find the diameter of the cylinder if the height is 42 cm. Use 3.14 for π
.(1 point)
Responses

30 inches
30 inches

15 inches
15 inches

5 inches
5 inches

10 inches

Answer 1

To find the diameter of the cylinder, we can use the formula for the volume of a right circular cylinder:

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

where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is approximately 3.14.

We are given:
- Volume \( V = 29,673 \) in³
- Height \( h = 42 \) cm

First, we need to convert the height from centimeters to inches because the volume is given in cubic inches. There are 2.54 cm in an inch, so:

\[
h = 42 \text{ cm} \times \frac{1 \text{ inch}}{2.54 \text{ cm}} \approx 16.54 \text{ inches}
\]

Now we can plug the values into the volume formula and solve for the radius \( r \):

\[
29,673 = 3.14 r^2 (16.54)
\]

Now, calculating \( 3.14 \times 16.54 \):

\[
3.14 \times 16.54 \approx 51.88
\]

Now rewrite the equation:

\[
29,673 = 51.88 r^2
\]

Next, divide both sides by 51.88 to find \( r^2 \):

\[
r^2 = \frac{29,673}{51.88} \approx 572.02
\]

Now take the square root of both sides to find \( r \):

\[
r \approx \sqrt{572.02} \approx 23.94 \text{ inches}
\]

Since the diameter \( d \) is twice the radius:

\[
d = 2r \approx 2 \times 23.94 \approx 47.88 \text{ inches}
\]

Now looking at the options you provided, it seems there might have been an error in volume or height interpretation, as it's clear the diameter is significantly larger than the options given (30 inches, 15 inches, 5 inches, 10 inches). Could you confirm the values or options?