Question

The external surface area of a hollow cylinder is $540\pi sq.cm$. Its internal diameter is $16cm$ and height is $15cm$. Find the total surface area.

• A. $1300\pi {cm}^2$
• B. $1320\pi {cm}^2$
• C. $1600\pi {cm}^2$
• D. None of these

Answer 1

The correct option is A $1300\pi {cm}^2$

External surface area of cylinder $=540\pi c{m}^2$

$2\pi Rh=540\pi c{m}^2$

Internal radius $\left(r\right)=\frac{16}{2}=8cm$

Height $\left(h\right)=15cm$

So,

$2\pi Rh=540\pi$

$2R\times 15=540$

$R\times 30=540$

$R=18cm$

Total surface area

$=2\pi (R+r)(R-r+h)$

$=2\pi \left(26\right)\left(25\right)$

$=1300\pi c{m}^2$

Hence, the total surface area of the cylinder $=1300\pi c{m}^2$.