Question

If the ratio of curved surface area and total surface area of a cylinder is 1:2. If total surface area of cylinder is 616cm*2 . Then find the volume of cylinder.

Answer 1

Answer:

Step-by-step explanation:

There is a cylinder...

Height : h

Radius : r

Curved surface area : $2\pi r*h$  → ( 1 )

Total surface area : $2\pi r(h+r)$  → ( 2 )

$h:(h+r)=1:2$ ( from ( 1 ), ( 2 ) )

$1(h+r)=2h\\h+r=2h\\h=r$

∴$h=r$

$2\pi r*2r=4r^2\pi =616$ ( total surface area of cylinder is 616 cm^2 )

$4r^2\pi =616\\r^2\pi =154\\\\r=\sqrt{\frac{154}{\pi } }$

$\pi r^2*h\\=\pi r^3\\=\frac{154}{\pi } *\sqrt{\frac{154}{\pi } }$

∴(Volume of cylinder) = $\frac{154}{\pi } *\sqrt{\frac{154}{\pi } }$ cm^3