Cones, Cylinders, & Spheres Unit Test
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Question
The volume of a sphere is 48 m3 . What is the volume of a cylinder if its radius is the same as the sphere’s and its height is equal to the sphere’s diameter?(1 point)
m3
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere.
In this case, the volume of the sphere is given as 48 m^3.
Therefore, we can set up the equation (4/3)πr^3 = 48 and solve for r:
(4/3)πr^3 = 48
r^3 = (48 * 3)/(4π)
r^3 = 144/π
Taking the cube root of both sides, we get:
r = (144/π)^(1/3)
The height of the cylinder is given as the diameter of the sphere, which is twice the radius. Therefore, the height of the cylinder is 2r.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the cylinder and h is its height.
Substituting the values of r and h, we get:
V = π(144/π)^(2/3)(2(144/π)^(1/3))
Simplifying, we get:
V = 2π(144/π)(144/π)^(2/3)
V = 2(144)^(5/3)π^(1/3)
Therefore, the volume of the cylinder is 2(144)^(5/3)π^(1/3) cubic meters.