To find the diameter of the right circular cylinder, we can use the formula for the volume of a cylinder, which is given by:
\[ V = \pi r^2 h \]
where:
- \( V \) is the volume (29,673 inches³),
- \( r \) is the radius,
- \( h \) is the height (42 cm).
Before substituting the values, we need to convert the height from centimeters to inches, since the volume is in cubic inches. There are 2.54 centimeters in an inch, so:
\[ h = \frac{42 \text{ cm}}{2.54} \approx 16.54 \text{ inches} \]
Now we can substitute into the volume formula:
\[ 29,673 = 3.14 r^2 (16.54) \]
Next, we can simplify and solve for \( r^2 \):
\[ 29,673 = 3.14 \times 16.54 \times r^2 \]
Calculating \( 3.14 \times 16.54 \):
\[ 3.14 \times 16.54 \approx 51.9616 \]
Thus, the equation becomes:
\[ 29,673 = 51.9616 r^2 \]
Now, we can solve for \( r^2 \):
\[ r^2 = \frac{29,673}{51.9616} \approx 571.55 \]
Taking the square root to find \( r \):
\[ r \approx \sqrt{571.55} \approx 23.93 \text{ inches} \]
Now, the diameter \( d \) is twice the radius:
\[ d = 2r \approx 2 \times 23.93 \approx 47.86 \text{ inches} \]
Considering the options you provided:
10 inches
30 inches
15 inches
5 inches
None of the options match the calculated diameter. Please review the information provided for any potential discrepancies or provide additional details if needed.