Question

If we have a cardboard sheet of area $32\pi m^2$ and we are supposed to create a cylindrical pen holder of radius $2m$ and height $3m$, then how many pen holders can be created using the provided cardboard sheet?

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B 2

Given that, the radius of the pen holder is $2m$.
The height of the pen holder is $3m$.
Area of the given cardboard sheet is $32\pi m^2$.

We know that, the curved surface area of a cylinder
$=2\pi rh$
Area of a circle $=\pi r^2$

Now, area of the cardboard sheet required to make 1 pen holder = CSA of cylinder + Area of base (circular in shape)

$=2\pi rh+\pi r^2$

$=12\pi +4\pi$

$=16\pi m^2$

Thus, total number of pen holders that can be created

$=\frac{\text{Area of cardboard sheet}}{\text{Cardboard sheet required to make 1 pen holder}}$

$=\frac{32\pi }{16\pi }$

$=2$