Question

The radius of the base and height of a cone are in the ratio of 3:4 and its volume is 324π cu.cm. Find its height.
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Answer 1

Answer:

A cone has a volume of 324 cu. cm, with a base radius and height ratio of 3:4. The height of the cone, is 12 cm.

Explanation:

Let the radius of the base be 3x and the height be 4x, where x is some positive constant. Then, the volume of the cone can be expressed as V = (1/3)π(3x)^2(4x) = 36πx^3.

Given that V = 324π cu.cm, we can solve for x as follows:

36πx^3 = 324π

x^3 = 9

x = 3

Therefore, the radius of the base is 3x = 9 cm and the height is 4x = 12 cm.

To verify that the volume of the cone is indeed 324π cu.cm, we can substitute the values of the radius and height into the formula for the volume of a cone:

V = (1/3)πr^2h = (1/3)π(9^2)(12) = 324π cu.cm.

Therefore, the height of the cone is 12 cm.

To know more about the concept please go through the links:

https://brainly.in/question/8069581

https://brainly.in/question/12304677

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