Question

7. The total surface area of a cylinder is 462 cm. Its curved surface area is
one-third of its total surface area. Find the volume of the cylinder.​

Answer 1

Answer: Volume of Cylinder : $539cm^{2}$

Step-by-step explanation:

Total Surface Area = $462cm^{2}$

2$\pi$r ( r + h ) = 462

C.S.A = $\frac{1}{3}$ T.S.A ---------1

Therefore CSA = $\frac{462}{3}$ = 154cm

⇒$TSA$=$2\pi rh + 2\pi$$r^{2}$  

⇒ $TSA$= $CSA$ + $2$$\pi$$r^{2}$

⇒$TSA$ = $\frac{TSA}{3}$  + $2$$\pi$$r^{2}$---------- From 1

⇒$\frac{2 TSA}{3}$ = $2$$\pi$$r^{2}$

⇒$\frac{TSA}{3}$ = $\pi$$r^{2}$

⇒ $\frac{462}{3}$ = $\frac{22}{7}$ $r^{2}$

∴ $r$ = $7cm$ -------- 2

Now CSA = 2$\pi$$rh$ = 154  . Put the values and you get :

h = $\frac{7}{2}$ ------- 3

Now :

Volume = $\pi r^{2}$h

Put the values from 1, 2 and 3. You will obtain the volume as :

$\pi r^{2} h = 539cm^{2}$

∴ Volume of the Cylinder is $539cm^{2}$.

Regards...

Took a lot of hardwork doing this. Brainliest would be appreciated :)