Question

The circumference of the base of a cylinder is 176 cm and its height is 30 cm. Find the volume of the cylinder.

Answer 1

Hint: We can find the radius of the cylinder from the circumference of the base using the equation for circumference of a circle. The height of the cylinder is also given. Then we can find the volume of the cylinder by substituting the values of radius and height in the equation for the volume of a cylinder.

Complete step by step solution: We know that base of a cylinder is circular. We have its circumference as 176cm. we can find the radius of the cylinder using the equation$C=2\pi r$.

 On substituting the values, we get,

$176=2\times {\displaystyle \frac{22}{7}}\times r$

On solving for r, we get,

$\Rightarrow r={\displaystyle \frac{176\times 7}{44}}$

On division we get,

$\Rightarrow r=4\times 7$

On multiplication we get,

$\Rightarrow r=28cm$.

Now we have the radius of the cylinder. We are also given the height of the cylinder is $30cm$. We know that the volume of a cylinder is given by the equation $V=\pi r^{2}h$.

On substituting the values of r and h, we get,

$\Rightarrow$$V={\displaystyle \frac{22}{7}}\times {\left(28\right)}^2\times 30$

On simplification, we get,

$\Rightarrow$$V=22\times 28\times 4\times 30$

After doing the multiplications, we get,

$\Rightarrow$$V=73,920c{m}^3$

So the volume of the given cylinder is $73,920c{m}^3$

Note: A cylinder is a three-dimensional object with 3 surfaces. One curved surface which is closed by two circular surfaces forms a cylinder. The volume of a body is the amount of space occupied by the body in a 3-dimensional space. As the given circumference is a multiple of 22, we take the value of $\pi$ as ${\displaystyle \frac{22}{7}}$ so that we won’t get a decimal value as the radius. As the radius is a multiple of 7, for finding the volume also, we take the value of $\pi$ as ${\displaystyle \frac{22}{7}}$, so that we get a whole number as the volume.