Question

A cylinder closed tin of radius r cm is made from 600cm2 tin sheet of metal.

a.show that it’s height h cm is given by h =300- pi r /pi r

Answer 1

Note: The expression "h =300- pi r /pi r" would equate to 299, as written. I find h = (300 - π
`r^(2)` )/πr to be the equation for height.

Explanation:

The total surface area of a sylinder is 2πr(h+r) where h is the height and r is the radius. That consists of top and bottom disks, each with an area of π
`r^(2)`, for a total of 2π
`r^(2)`. The side is a continous sheet that has an area of 2πrh, where h is the height. 2πr is the circumference of the can, so the surface area of the side is 2πrh.

The total surace area of a closed cylinder is therefore 2π
`r^(2)` + 2πrh.

2π
`r^(2)` + 2πrh = 600

π
`r^(2)` + πrh = 300

πrh = 300 - π
`r^(2)`

h = (300 - π
`r^(2)` )/πr