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 = 2 пrh + 2 пr^2

Given radius of first cylinder is 20cm

given height of the first cylinder is 2 cm

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

= 2 п (20) (2) + 2 п (2) ^2

= 4 п (20+2)

The surface area of first cylinder is 88 п

Step 2:

given data The surface area of first cylinder is 88 п 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 = 2 пrh + 2 пr^2 = 88 п

2 п (4) h+2 п (4) ^2 = 88 п

on simplification we get

2 п (4h+16) = 88 п

after cancellation '2 п' 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