Question

If a sheet of paper of length 10 cm and breadth 5 cm is rolled along its length to form a cylinder, then the space inside the cylinder is .

• A. 39.809 $c{m}^3$​
• B. 35 $c{m}^3$​
• C. 42 $c{m}^3$​

Answer 1

The correct option is A 39.809 $c{m}^3$​

When a rectangle is rolled across the length, the height of the formed cylinder will be equal to the breadth of the rectangle, i.e. 5 cm.
And, the length of the rectangle will be equal to the circumference of the circular base of the cylinder, i.e. 10 cm.
Thus, using that we can find the radius of a cylinder as

$2\pi r=10\Rightarrow r=\frac{10}{2\pi }\Rightarrow r=\frac{5}{\pi }cm$

Thus, volume of cylinder
$=\pi r^{2}h=3.14\times {\left(\frac{5}{3.14}\right)}^2\times 5=\frac{125}{3.14}=39.809c{m}^3$