Maths-
General
Easy

Question

The sum of the radius and height of a cylinder is 21 cm and the T.S.A of the cylinder is 660 sq. cm. Find the height and volume of the cylinder ?

hintHint:

We take suitable variables for height and radius. Put it in the formula for TSA and find the required parameters.

The correct answer is: The height of the cylinder is 16 cm and the volume is 400π cm3.


    Explanations:
    Step 1 of 2:
    Let the height of the cylinder be h .
    Sum of the radius and height is 21 cm, so the radius will be  left parenthesis 21 minus h right parenthesis cm.
    Given, TSA of the cylinder = 660
    not stretchy rightwards double arrow 2 pi r left parenthesis r plus h right parenthesis equals 660
    not stretchy rightwards double arrow 2 pi left parenthesis 21 minus h right parenthesis left parenthesis 21 minus h plus h right parenthesis equals 660
    not stretchy rightwards double arrow 2 pi left parenthesis 21 minus h right parenthesis cross times 21 equals 660
    not stretchy rightwards double arrow 21 minus h equals fraction numerator 660 over denominator 2 cross times 21 end fraction cross times 7 over 22
    not stretchy rightwards double arrow h equals 21 minus open parentheses fraction numerator 660 over denominator 2 cross times 21 end fraction cross times 7 over 22 close parentheses
    not stretchy rightwards double arrow h equals 16 cm
    So, r = 21 – 16= 5 cm
    Step 2 of 2:
    Volume of the cylinder =pi r squared h
    equals pi left parenthesis 5 right parenthesis squared cross times 16 equals 400 pi cm3
    Final Answer:
    The height of the cylinder is 16 cm and the volume is 400pi cm3.

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