Question

The ratio of curved surface area to the total surface area of right circular cylinder is 1:3. Find the volume of the cylinder if its total surface area is 1848cm 2 . [ pie =22/7 ]

Answer 1

Given
C.S.A. : T.S.A.= 1:3
⇒2$\pi$rh : 2$\pi$r(h+r)= 1:3
⇒h/(h+r)=1/3
⇒3h=h+r
⇒2h=r

Now it's given that 2$\pi$r(h+r)=1814 cm²
⇒2π×2h×(h+2h)=1848 cm²
⇒12πh²=1848 cm²
⇒h²=1848/12π cm²
⇒h²= 49 cm²
⇒h=7 cm
⇒r=2×7 cm= 14 cm
volume=πr²h
=22×14×14×7/7 cm³
=4312 cm³