Question

A rectangular sheet of paper 22 cm long and 10 cm broad can be curved to form the lateral surface area of a right circular cylinder in two ways Then the difference between the volumes of the two cylinders thus formed is

• A. $200$ $c{m}^3$
• B. $210$ $c{m}^3$
• C. $250$ $c{m}^3$
• D. $252$ $c{m}^3$

Answer 1

The correct option is B $210$ $c{m}^3$

The rectangle sheet of paper is 22 cm long and 10 cm broad

Then volume of first right circular cylinder =$\pi r^{2}h=\pi {\left(\frac{7}{2}\right)}^2\times 12c{m}^3$

And volume of second right circular cylinder =$\pi r^{2}h=\pi {\left(\frac{21}{11}\right)}^2\times 22c{m}^3$
then diff of volume of two cylinders=$\pi {\left(\frac{7}{2}\right)}^2\times 12-\pi {\left(\frac{21}{11}\right)}^2\times 22$

$\frac{22}{7}\times 7\times 7\times 3(1-\frac{3\times 2}{11})=210c{m}^3$