A cylinder has a radius of 20 cm and a height of 2 cm. Find the height of another cylinder that has a radius of 4 cm and the same surface area as the first cylinder.

The height of the another cylinder 'h'  = 7

Step-by-step explanation:

Explanation:-

Step 1:-

Surface area of the cylinder  = 2пrh + 2пr^2

Given radius of first cylinder is 20cm

given height of the first cylinder is 2 cm

The surface area of first cylinder is = 2пrh + 2пr^2

                                                          = 2п(20)(2)+2п(2)^2

                                                          = 4п(20+2)

The surface area of first cylinder is  88п

Step 2:

given data The surface area of first cylinder is  88п is same as second cylinder also

Find the height of the second cylinder

Given Radius of the second cylinder r = 4

Surface area of the cylinder  = 2пrh + 2пr^2 = 88п

                                                   2п(4)h+2п(4)^2 =88п

on simplification we get

                                   2п (4h+16) = 88п

after cancellation '2п' value and on simplification, we get

                                    4h+16 = 44

                                    4h = 44-16

                                  4h = 28

                                 h=7

Therefore the height of the another cylinder is 'h' =7

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