A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21 meters cubed. A sphere with height h and radius r. A cylinder with height h and radius r. What is the volume of the sphere?
Mathematics · High School · Mon Jan 18 2021
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Given the statement:
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21 meters cubed. A sphere with height h and radius r. A cylinder with height h and radius r.
Determine the volume of the sphere.
Formula for the volume of the cylinder:
V=πr^2h
Formula for the volume of the sphere:
V=4/3πr^3
Solution:
In order to find for the volume of the sphere, we must first find the radius of the cylinder, which is equal to its own height, and equal to the radius of the sphere, therefore, we can rewrite the formula for the volume of the cylinder as,
V=πr^3
21 m^3 = πr^3
Divide both sides by pi.
21m^3/π = πr^3/π
r^3 = 21m^3/π
Take the cube root of both sides.
r = (21m^3/π)^⅓
r = 1.9 m
Solve for the volume of the sphere.
V=4/3πr^3
V=4/3π(1.9m)^3
V = 2.9 m^3
Final answer:
The volume of the sphere is 2.9 m^3.