Question

There is a hollow cylinder as shown in figure having an inner and outer radius as 7 cm and 14 cm respectively and height is 28 cm. A man wants to paint it completely inside out. The area which he needs to paint is equal to:

• A. $4640c{m}^2$
  
• B. $4620c{m}^2$
• C. $5260c{m}^2$
• D. $4820c{m}^2$

Answer 1

The correct option is B

$4620c{m}^2$

Let $r_1$ be the inner radius and $r_2$ be the outer radius and $h$ be the height.
Total area which needs to be painted will be equal to inner curved surface area + outer curved surface area + 2(base area), which is nothing but the total surface area of the hollow cylinder.
Required area $=2\pi r_{1}h+2\pi r_{2}h+2\left(\pi \right(r_2{)}^2-\pi \left(r_1{)}^2\right)$
$=2\pi h(r_1+r_2)+2\pi (r_2^2-r_1^2)$
$=2\pi h(r_1+r_2)+2\pi (r_2-r_1)(r_2+r_1)$
$=2\pi (r_1+r_2)[h+r_2-r_1]$
Substituting the value, we get
$2\times \frac{22}{7}\times (14+7)(28+14-7)=4620c{m}^2$