Q. 54

# The ratio between

Given: The ratio between the radius of the base and the height of the cylinder is 2: 3.

Volume of the Cylinder is 1617cm3

Let 2x and 3x be radius and height of the Cylinder respectively.

Volume of the Cylinder is given as: πr2h

πr2h = 1617

π × (2x)2 × (3x) = 1617

12π × x3 = 1617

x3 = = =

x = () =

r = 2 × = 7cm

and, h = 3 × = 10.5 cm

Total surface area of a cylinder is: 2πrh(r + h)

Let S be the TSA of a cylinder

S = 2πrh(r + h)

S = 2 × π × (7) × (7 + 10.5) = 2 × π × (7) × 17.5 = 770

S = 770cm2

That is, Total surface area of the cylinder is 770 cm2

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