Maths-
General
Easy

Question

The difference between the outer and inner curved surface areas of a 14 cm long cylinder is 88 sq.cm Find the outer and inner radii of the cylinder given that the volume of the metal is 176 cubic cm

hintHint:

Forming the equations based on the given information, we will get two equations. Then we will find the radii by solving those two equations.

The correct answer is: The outer and inner radii of the cylinder are 2.5 cm and 1.5 cm


    Explanations:
    Step 1 of 3:
    Given, outer CSA – inner CSA = 88
    not stretchy rightwards double arrow 2 pi h left parenthesis R minus r right parenthesis equals 88, where  = length of cylinder,  R = outer radius, r = inner radius
    not stretchy rightwards double arrow R minus r equals 88 cross times 1 half cross times 7 over 22 cross times 1 over 14
    not stretchy rightwards double arrow R minus r equals 1…(i)
    Step 2 of 3:
    Also, given volume with  R – volume with  r = 176
    not stretchy rightwards double arrow pi h open parentheses R squared minus r squared close parentheses equals 176
    not stretchy rightwards double arrow pi cross times 14 cross times left parenthesis R plus r right parenthesis left parenthesis R minus r right parenthesis equals 176
    not stretchy rightwards double arrow R plus r equals 176 cross times 7 over 22 cross times 1 over 14 comma text  since  end text R minus r equals 1 comma text  from equation (i)  end text
    not stretchy rightwards double arrow R plus r equals 4…(ii)
    Step 3 of 3:
    Adding (i) and (ii), we get
    R plus r plus R minus r equals 4 plus 1
    not stretchy rightwards double arrow 2 R equals 5
    not stretchy rightwards double arrow R equals 5 over 2 equals 2.5 cm
    Putting R = 5/2 in equation (ii), we get
    5 over 2 plus r equals 4
    not stretchy rightwards double arrow r equals 4 minus 5 over 2 equals 3 over 2 equals 1.5 cm
    Final Answer:
    The outer and inner radii of the cylinder are 2.5 cm and 1.5 cm

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