Maths-
General
Easy

Question

The ratio of the diameter and height of a cylinder is 4 : 5. Find the height of the cylinder, if its volume is 540π cubic units.

hintHint:

We take the common ratio be x and recalling the formulae, we solve the problem.

The correct answer is: The height of the cylinder is 15 units.


    Explanations:
    Step 1 of 2:
    Let the common ratio be x.
    The diameter of the cylinder = 4x. Therefore, the base radius, r = 4x/2 = 2x units
    And the height of the cylinder = 5x units.
    So, volume of the cylinder = pi left parenthesis 2 x right parenthesis squared 5 x cube units
    Step 2 of 2:
    Given, pi left parenthesis 2 x right parenthesis squared 5 x equals 540 pi
    not stretchy rightwards double arrow 4 x squared cross times 5 x equals 540
    not stretchy rightwards double arrow 20 x cubed equals 540
    not stretchy rightwards double arrow x cubed equals 27
    not stretchy rightwards double arrow x equals 3
    So, the height of the cylinder equals 5 cross times 3 = 15 units.
    Final Answer:
    The height of the cylinder is 15 units.

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