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.
To find the diameter of the cylinder, we can use the formula for the volume of a cylinder:
V = πr^2h
Given that the volume is 29,673 inches3 and the height is 42 cm, we can convert the height to inches by multiplying by 2.54:
42 cm * 2.54 = 106.68 inches
Now we can plug in the values and solve for the radius (r):
29,673 = 3.14r^2 * 106.68
29,673 = 334.9872r^2
r^2 = 88.501
r = √88.501
r ≈ 9.4 inches
Now that we have found the radius, we can find the diameter by multiplying by 2:
d = 2r
d = 2 * 9.4
d ≈ 18.8 inches
Therefore, the diameter of the cylinder is approximately 18.8 inches.