To calculate the height of the can, we'll use the formula for the volume of a cylinder, which is given by:
\[ V = \pi r^2 h \]
Where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height.
- First, let's find the radius of the can. The diameter is given as 4 inches, so the radius \( r \) is half of the diameter:
\[ r = \frac{d}{2} = \frac{4}{2} = 2 \text{ inches} \]
- Next, we can substitute the known values into the volume formula. We know the volume \( V = 450 \) cubic inches, and we have calculated \( r = 2 \) inches:
\[ 450 = \pi (2)^2 h \]
- Now, calculate \( (2)^2 \):
\[ (2)^2 = 4 \]
- Substitute this back into the equation:
\[ 450 = \pi (4) h \]
- Now, divide both sides by \( 4\pi \) to solve for \( h \):
\[ h = \frac{450}{4\pi} \]
- Calculate \( 4\pi \):
\[ 4\pi \approx 12.5664 \]
- Substitute this value back in:
\[ h = \frac{450}{12.5664} \approx 35.8 \text{ inches} \]
Therefore, the height of the can, to the nearest tenth of an inch, is approximately \( 35.8 \) inches.
So the correct response is:
35.8 in