The volume of a right circular cylinder is 29,673 inches3 . Find the diameter of the cylinder if the height is 42 cm. Use 3.14 for π
First, we need to convert the height from centimeters to inches.
1 cm = 0.3937 inches
42 cm * 0.3937 = 16.5354 inches
Now we can use the formula for the volume of a cylinder:
V = πr^2h
Where V is the volume, r is the radius, h is the height.
Since the diameter is twice the radius, we can find the diameter first:
V = π(d/2)^2 * 16.5354
29,673 = π(d/2)^2 * 16.5354
29,673 / (π*16.5354) = (d/2)^2
565.15 = (d/2)^2
565.15 * 2 = d^2
d = √1130.3
d ≈ 33.6 inches
Therefore, the diameter of the cylinder is approximately 33.6 inches.