Question

The radius and height of a cylinder are in the ratio 7:2.
If the volume the cylinder is
8316cm^3,find the total surface area of the cylinder.

Answer 1

Since the ratio between radius and height is 7 : 2, let the radius and height be 7x and 2x respectively.

Now, We know that the volume of a cylinder can be related as follows:
Volume of the cylinder, V = π * r ^ 2 * h

Substituting the variables we assumed in the beginning of the answer,
Volume of cylinder, V = π * ( 7x ) ^ 2 * 2x
V = ( 22 / 7 ) * ( 49x ^ 2 ) * 2x
8316 = 22 * ( 7x ^ 2 ) * 2x
8316 / 22 = 14x ^ 3

Exchanging LHS and RHS,

14x ^ 3 = 378
x ^ 3 = 378 / 14
x ^ 3 = 27

$\bold{x = \sqrt[3]{27} }$

Hence,
x = 3

Radius of the cylinder, r = 7x = 7 * 3 = 21 cm
Height of the cylinder, h = 2x = 2 * 3 = 6 cm

TSA of cylinder = 2 * π * r^2 + 2 * π * h
TSA = 2 ( 22 / 7 ) * ( 21 ) ^ 2 + 2 ( 22 / 7 ) * 6
TSA = ( 44 / 7 ) * 441 + ( 44 / 7 ) * 6
TSA = 44 * 63 + 264 / 7
TSA = 2772 + 264 / 7
TSA = ( 19404 + 264 ) / 7
TSA = 19668 / 7
TSA = 2809.71 ( approx. )

Answer 2

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