To estimate the volume of a cylinder with the given radius and height, we will use the formula:
\[ V = \pi r^2 h \]
where:
- \( r = 3.75 \) inches
- \( h = 6.21 \) inches
First, round the values to the nearest whole number:
- \( r \approx 4 \) inches (since 3.75 rounds to 4)
- \( h \approx 6 \) inches (since 6.21 rounds to 6)
Now, substitute the rounded values into the formula:
\[ V \approx \pi (4)^2 (6) \]
Calculating \( (4)^2 \):
\[ (4)^2 = 16 \]
Now, substitute this back into the volume formula:
\[ V \approx \pi \cdot 16 \cdot 6 \]
Calculating \( 16 \cdot 6 \):
\[ 16 \cdot 6 = 96 \]
Thus, the volume approximation becomes:
\[ V \approx 96\pi \]
Now, using the approximate value of \( \pi \approx 3.14 \):
\[ V \approx 96 \cdot 3.14 \]
Calculating that:
\[ 96 \cdot 3.14 \approx 301.44 \]
Now, rounding \( 301.44 \) to the nearest whole number gives us:
\[ V \approx 301 \]
Therefore, the estimate of the volume of the cylinder is approximately 301 cubic inches.