Question

The amount of cardboard needed to build a closed cylindrical box of given dimensions is sq. in.

(Take $\pi$ = 3.14)

• A. 113.04
• B. 168.76
• C. 138.16
• D. 254.34

Answer 1

The correct option is C 138.16

On opening the cylinder and visualizing it we get:

Here,
Diameter of cylinder = 4 in

$\text{Radius (r) =}\frac{\text{diameter}}{2}=\frac{4}{2}$
= 2 in

Height of cylinder (h) = 9 in

The amount of cardboard needed is the surface area of the cylinder having the same dimensions.

Total surface area = Area of 2 circles + Area of rectangle

$\therefore \text{Surface area of cylinder =}2\pi r^2+2\pi rh$
$=(2\times 3.14\times 2^2)+(2\times 3.14\times 2\times 9)$
$=25.12+113.04$
$=138.16sq.in$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ∴ Amount of cardboard required = 138.16 sq. in