Question

If solid cylinder has total surface area $1000{cm}^2$ and its curved surface area is $\frac{1}{4}$ of $d$. What is the volume of cylinder?

• A. $125\pi$
• B. $\sqrt{375}\pi$
• C. $125\sqrt{375}$
• D. $125\sqrt{375}\pi$

Answer 1

Answer: (D)

$125\sqrt{375}\pi$

Let radius and height be $r$ and $h$ of cylinder
Total surface area $=1000{cm}^2$

$2\pi r(r+h)=1000{cm}^2$......(i)

Lateral surface area of cylinder $=$ $\frac{1}{4}\times$ total SA

From (i), we have

$2\pi rh=\frac{1}{4}\times 1000=250$.....(ii)

$\Rightarrow 2\pi rh+2\pi r^2=1000250+2\pi r^2=1000$

$\Rightarrow 2\pi r^2=750$

$\Rightarrow \pi r^2=375$

Volume of cylinder $\pi r^{2}h=375h$

$=375\times \frac{250}{2\sqrt{375}}$

$=125\sqrt{375}\pi$