Question

The difference between the outer curved surface area and the inner curved surface area of a hollow cylinder is $352$ $c{m}^2.$ If its height is $28$ cm and the volume of material in it is $704$ $c{m}^3;$ find its external curved surface area.

• A. $528$ $c{m}^2$
• B. $520$ $c{m}^2$
• C. $525$ $c{m}^2$
• D. $527$ $c{m}^2$

Answer 1

The correct option is A $528$ $c{m}^2$

Let $r_1=$ outer surface area, $r_2=$ inner surface area, length $h=28$
Outer curved surface area of cylinder $=2\pi r_{1}hc{m}^2$
Inner curved surface area of cylinder $=2\pi r_{2}hc{m}^2$
Difference between two curved surface area cylinder $=2\pi \left(28\right)(r_1-r_2)=352c{m}^2$
$r_1-r_2=2$.......(1)
Volume of cylinder $=\pi (r_1^2-r_2^2)h=\pi (r_1^2-r_2^2)\left(28\right)=704$
$r_1^2-r_2^2=8$.....(2)
Solving, $\left(2\right),(r_1-r_2)(r_1+r_2)=8$
$2(r_1+r_2)=8$
$r_1+r_2=4$.....(3)
From (1) and (3), $r_1=3,r_2=1$
External curved surface $=2\pi rh=2\pi \left(3\right)\left(28\right)=528c{m}^2$