RRB Group D 10-Dec-2018 Shift 1 Solved Paper

Question : 25 of 100

Marks: +1, -0

The radius of a sphere equal to thrice the radius of the base of a cylinder. The height of the cylinder is nine times the radius of its base. If the numerical values of the total surface area of the cylinder and that of the volume of the sphere are the same, what is the height of the cylinder?

4.5 units
3 units
2.25 units
5 units

Validate

Solution:

Radius of sphere = R = 3r
Radius of the base of cylinder = r
and height 'h'’ = 9r
Total surface area of cylinder=

2πrh+πr^2

=2πr(9r)+πr^2

=18πr^2+πr^2=20πr^2

....(1)
Volume of sphere=

4/3πR^3

....(2)
Equation (1)= Equation (2)

20πr^2=4/3πR^3

20πr^2=4/3π(3r)^3

20πr^2=4/3π×27r^3

r={20×3}/{4×27}=5/9

h=92=9×5/9=5

units

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