The base radius of cylinder is twice the base radius of cylinder , and the height of cylinder is twice the height of cylinder . What is the ratio of the volume of cylinder to the volume of cylinder ?
Question
The base radius of cylinder is twice the base radius of cylinder , and the height of cylinder is twice the height of cylinder . What is the ratio of the volume of cylinder to the volume of cylinder ?
Solution
The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder.
Let's denote the radius and height of cylinder A as r1 and h1, and the radius and height of cylinder B as r2 and h2.
Given that the base radius of cylinder A is twice the base radius of cylinder B, we have r1 = 2r2.
Also, the height of cylinder A is twice the height of cylinder B, so h1 = 2h2.
The volume of cylinder A is then V1 = π(2r2)²(2h2) = 8πr2²h2.
The volume of cylinder B is V2 = πr2²h2.
The ratio of the volume of cylinder A to the volume of cylinder B is then V1/V2 = (8πr2²h2) / (πr2²h2) = 8.
So, the volume of cylinder A is 8 times the volume of cylinder B.
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