Question
The volume of a right circular cylinder is 3,140 in.3
. Find the radius of the cylinder if the height is 10 in. Use 3.14
for π
.(1 point)
in.
. Find the radius of the cylinder if the height is 10 in. Use 3.14
for π
.(1 point)
in.
Answers
GPT-4o mini
The volume \( V \) of a right circular cylinder can be calculated using the formula:
\[
V = \pi r^2 h
\]
where \( r \) is the radius, \( h \) is the height, and \( \pi \) is approximately 3.14. Given that the volume \( V \) is 3140 in³ and the height \( h \) is 10 in, we can substitute these values into the formula to find the radius \( r \):
\[
3140 = 3.14 \cdot r^2 \cdot 10
\]
First, simplify the equation:
\[
3140 = 31.4 \cdot r^2
\]
Next, divide both sides by 31.4 to solve for \( r^2 \):
\[
r^2 = \frac{3140}{31.4}
\]
Calculating this gives:
\[
r^2 = 100
\]
Now, take the square root of both sides to find \( r \):
\[
r = \sqrt{100} = 10 \text{ in}
\]
Thus, the radius of the cylinder is:
\[
\boxed{10 \text{ in}}
\]
\[
V = \pi r^2 h
\]
where \( r \) is the radius, \( h \) is the height, and \( \pi \) is approximately 3.14. Given that the volume \( V \) is 3140 in³ and the height \( h \) is 10 in, we can substitute these values into the formula to find the radius \( r \):
\[
3140 = 3.14 \cdot r^2 \cdot 10
\]
First, simplify the equation:
\[
3140 = 31.4 \cdot r^2
\]
Next, divide both sides by 31.4 to solve for \( r^2 \):
\[
r^2 = \frac{3140}{31.4}
\]
Calculating this gives:
\[
r^2 = 100
\]
Now, take the square root of both sides to find \( r \):
\[
r = \sqrt{100} = 10 \text{ in}
\]
Thus, the radius of the cylinder is:
\[
\boxed{10 \text{ in}}
\]