Question

10. A rectangular paper has dimensions 15 cm x 3 cm. It is revolved about its width. Find the volume of the
cylinder so obtained.​

Answer 1

Given

• Rectangle Paper Of Dimensions 15cm × 3cm
• it's Revolved About It's width.

To Find

• Volume of Cylinder So Obtained.

★ If the sheet is folded to form a cylinder then the length becomes the height and the width becomes the circumference of the cylinder base.

★The height of the cylinder will be the length of the long side of your paper, so H = 15cm. Now we need the radius of the circular base.

★The width of the paper will be equal to the width of the circle that forms the base of the cylinder. Use this to find circle length:

• Circumference of Circle = 2πr

${\implies \sf \: 15cm \: = 2\pi \ r}$

${\implies \sf \: \frac{15}{2} cm \: = \pi \ r}$

${\implies \sf \: r = \dfrac{15}{2\pi} }$

We Know That,

• Volume Of Cylinder= πr²h

${ \sf \: Volume \: Of \: Cylinder= πr²h }$

${ \sf \: Volume \: Of \: Cylinder= \pi \left( \frac{15}{2\pi} \right) ^{2} \times 3}$

${ \sf \: Volume \: Of \: Cylinder= \pi \left( \frac{7.5}{\pi} \right) ^{2} \times 3}$

${ \sf \: Volume \: Of \: Cylinder= \pi \times \frac{56.25}{\pi ^{2} } \times 3}$

${ \sf \: Volume \: Of \: Cylinder= \dfrac{56.25}{3.14 } \times 3}$

${ \sf \: Volume \: Of \: Cylinder= 17.91 \times 3}$

• $\underline{\boxed{{ \sf \: Volume \: Of \: Cylinder= 53.74cm ^{3}} }}$