You need to remember that the total surface of cylinder is the sum of two times area of base and the surface area of lateral part such that:
TSA = 2A base + `h*(2pi*r)`
You need to evaluate TSA of cylinder that has the height H and the radius r such that:
`TSA_(H,r) = 2*pi*r^2 + 2H*pi*r`
You need to factor out `2pi*r` such that:
`TSA_(H,r) = 2pi*r(r + H)`
The problem provides the information that `TSA_(H,r)` is double of `TSA_(h,r).`
You need to evaluate `TSA_(h,r)` such that:
`TSA_(h,r) = 2pi*r(r + h)`
If you multiply by 2 both sides yields:
`2TSA_(h,r) = 4pi*r(r + h)`
Since `TSA_(H,r) = 2TSA_(h,r),` then you may substitute `TSA_(H,r)` for `2TSA_(h,r)` such that:
`2pi*r(r + H) = 4pi*r(r + h)`
You need to divide by `2pi*r` both sides such that:
`(r + H) = 2(r + h) `
You need to open the brackets such that:
`r + H = 2r + 2h`
You need to isolate 2h to one side such that:
`r + H - 2r = 2h`
`H - r = 2h`
You need to divide by 2 such that:
`h = (H-r)/2`
The last line proves what problem demands, hence `h = (H-r)/2` under given conditions.
See eNotes Ad-Free
Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.
Already a member? Log in here.