Question

The height of cylinder a is 32 feet and the height of a cylinder b is 24 feet . If the cylinders are similar , find the surface area ratio of cylinder a to cylinder b

Answer 1

The surface area ration of Cylinder A to Cylinder B is 16:9

Answer 2

The surface area ratio of cylinder a to cylinder b is
`(16)/(9)`

Explanation:

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

The scale factor is equal to the ratio of its corresponding sides

so

Let

z------> the scale factor

x------> surface area of cylinder a

y------> surface area of cylinder b

`z^(2)=(x)/(y)`

step 1

Find the scale factor

`z=(32)/(24)=(4)/(3)`

step 2

Find the ratio of the surface areas

`z^(2)=(x)/(y)`

we have

`z=(4)/(3)`

substitute

`((4)/(3))^(2)=(x)/(y)`

`(x)/(y)=(16)/(9)`