Question

A rectangular piece of paper $11cm\times 4$ cm is folded without overlapping to make a cylinder of height $4$ cm. Find the volume of the cylinder.

• A. $38.5c{m}^3$
• B. $40.5c{m}^3$
• C. $41.5c{m}^3$
• D. $42.5c{m}^3$

Answer 1

The correct option is B $40.5c{m}^3$

REF.Image

Length = 11 cm

Breadth = 4 cm.

When the rectangle is converted into a cylindrical shape

Since the rectangle is rolled along it's width to make cylinder.

Height of cylinder = Width of rectangle = 4 cm

Let the radius of the cylinder be r

$\therefore$ Perimeter of the cylinder = length of the rectangle.

So by the formula of circumference circle

$2\pi r=11$

$\Rightarrow 2\times \frac{22}{7}\times r=11$

$\Rightarrow \frac{44}{7}\times r=11$

$\Rightarrow r=11\times \frac{7}{44}=\frac{7}{4}$

Volume of cylinder = $\pi r^{2}h$

$=\frac{22}{7}\times \frac{7}{4}\times \frac{7}{4}\times 4$

$=\frac{77}{2}=38.5c{m}^3$