Question

The sum of the altitude and the base radius of a cylinder is `63 cm`. The radius is `4/5` as long as the altitude. Calculate the surface area volume of the cylinder?

Answer 1

Surface area of cylinder is `5544` sq.cm. and Volume of cylinder is `86240` cc.

Explanation:

Let the altitude be `h`, as radius is `4/5` of height, it is `(4h)/5`. But sum of altitude and radius is `63`, hence

`h+(4h)/5=63` or `(5h)/5+(4h)/5=63` or `(9h)/5=63`

Therefore `h=63xx5/9=7cancel(63)xx5/cancel9=35`

Hence altitude is `35` cm and radius is `63-35=28` cm.

Assume pi=22/7#, hence surface area of cylinder given by

`pir(r+h)=22/7xx28xx63`

= `22/cancel7xx4cancel(28)xx63=88xx63=5544` sq.cm.

Volume of cylinder is `pir^2h=22/7xx28xx28xx35`

= `22/cancel7xx4cancel(28)xx28xx35=86240` cc.