Question
cylinder with 549.5 cubic inches in volume is 7 inches tall. What is the radius of the cylinder?
Use 3.14 for π
Use 3.14 for π
Answers
Answered by
GPT-4o mini
The volume \( V \) of a cylinder can be calculated using the formula:
\[
V = \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height. Given that the volume is \( V = 549.5 \) cubic inches and the height \( h = 7 \) inches, we can rearrange the formula to solve for the radius \( r \):
1. Substitute the known values into the formula:
\[
549.5 = 3.14 r^2 \cdot 7
\]
2. Simplify the equation:
\[
549.5 = 21.98 r^2
\]
3. Divide both sides by 21.98 to isolate \( r^2 \):
\[
r^2 = \frac{549.5}{21.98}
\]
Calculating the right side:
\[
r^2 \approx 25
\]
4. Take the square root of both sides to find \( r \):
\[
r \approx \sqrt{25}
\]
\[
r \approx 5
\]
Thus, the radius of the cylinder is approximately **5 inches**.
\[
V = \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height. Given that the volume is \( V = 549.5 \) cubic inches and the height \( h = 7 \) inches, we can rearrange the formula to solve for the radius \( r \):
1. Substitute the known values into the formula:
\[
549.5 = 3.14 r^2 \cdot 7
\]
2. Simplify the equation:
\[
549.5 = 21.98 r^2
\]
3. Divide both sides by 21.98 to isolate \( r^2 \):
\[
r^2 = \frac{549.5}{21.98}
\]
Calculating the right side:
\[
r^2 \approx 25
\]
4. Take the square root of both sides to find \( r \):
\[
r \approx \sqrt{25}
\]
\[
r \approx 5
\]
Thus, the radius of the cylinder is approximately **5 inches**.
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