A rectangular piece of paper 66 cm long and 15 cm broad, is rolled along its length to form a cylinder. What is the radius of the cylinder? What is the volume of the cylinder?

Given: A rectangular piece of paper 66 cm long and 15 cm broad, is rolled along its length to form a cylinder. 

To find: Here we have to find the radius and volume of the cylinder.

Solution:

Length of rectangle = 66 cm

Breadth of rectangle = 15 cm

The piece of paper is rolled along the length to form a cylinder, then, the circumference of the base circle is equal to the length of the paper. And the height of the cylinder is equal to the breadth of the rectangle.

So,

Circumference of circle = Length of the rectangle

$2πr\ =\ 66$

$2\ \times \ \frac{22}{7} \ \times \ r\ =\ 66$

$r\ =\ 66\ \times \ \frac{7}{22} \ \times \ \frac{1}{2}$

$\mathbf{r\ =\ 10.5\ cm}$

Now,

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

Volume of cylinder = $\frac{22}{7} \ \times \ ( 10.5)^{2} \ \times \ 15$

Volume of cylinder = $\frac{22}{7} \ \times \ 110.25\ \times \ 15$

Volume of cylinder = $22\ \times \ 15.75\ \times \ 15$

Volume of cylinder = 5197.50 cm³

So, the radius and volume of the cylinder are 10.5 cm and 5197.50 cm³ respectively.

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Updated on: 10-Oct-2022

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