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Answer:
The volume of the sphere is 14m³
Step-by-step explanation:
Given
Volume of the cylinder =
Required
Volume of the sphere
Given that the volume of the cylinder is 21, the first step is to solve for the radius of the cylinder;
<em>Using the volume formula of a cylinder</em>
The formula goes thus
Substitute 21 for V; this gives
Divide both sides by h
The next step is to solve for the volume of the sphere using the following formula;
Divide both sides by r
Expand Expression
Substitute
Multiply both sided by r
------ equation 1
From the question, we were given that the height of the cylinder and the sphere have equal value;
This implies that the height of the cylinder equals the diameter of the sphere. In other words
, where D represents diameter of the sphere
Recall that
So,
Substitute 2r for h in equation 1
Hence, the volume of the sphere is 14m³