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Question

The base radius of a cylinder is 5/3 times its height. The cost of painting its C.S.A. at 2 paise/cm2 is Rs 92.40. What volume of the paint is required?

hintHint:

The CSA of a cylinder is 2 pi r h , where  and  are the base radius and height of the cylinder, respectively. Rate of cost for painting is (total cost/CSA). The volume of a cylinder is given by,pi r squared h.

The correct answer is: The volume of the cylinder is 80.85 cm3


    Explanations:
    Step 1 of 3:
    The rate of cost of painting is given by 2 paise/cm2 and the total cost is Rs 92.40.
    Therefore, the CSA of the cylinder is 92.40/2 = 46.2 cm2.
    Step 2 of 3:
    Let base height be h. Then, base radius of the cylinder will be 5 h divided by 3 .
    We have, 2 pi r h equals 46.2
    not stretchy rightwards double arrow 2 pi cross times fraction numerator 5 h over denominator 3 end fraction cross times h equals 46.2
    not stretchy rightwards double arrow h squared equals 462 over 10 cross times 7 over 22 cross times 1 half cross times 3 over 5
    not stretchy rightwards double arrow h squared equals 4.41
    not stretchy rightwards double arrow h equals 2.1,discarding the negative value since distance must be positive
    therefore r equals 5 over 3 cross times 2.1 equals 3.5 cm
    Step 3 of 3:
    The volume of cylinder
    equals pi cross times 3.5 squared cross times 2.1
    equals 80.85 cm cubed
    Final Answer:
    The volume of the cylinder is 80.85 cm3

    There is a small typo present in this question. We have to find the volume of the cylinder not of the paint.

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