Question

The volume of the cylinder is 330 \[c{{m}^{3}}\] . If the length of the cylinder is 4 cm, calculate the radius of the cross section. $\left( \pi =3.142 \right)$
(A). 5.12 cm
(B). 7.12 cm
(C). 4.12 cm
(D). None of these

Answer 1

Hint: We have been given the volume and height of a cylinder. We know the formula for finding the volume of a cylinder. Thus, it is a direct substitution of the values and find radius.

Complete step-by-step solution -
We have been given the volume of the cylinder as 300$c{{m}^{3}}$ . We can take the volume of the cylinder as ‘v’.
Therefore, volume of the cylinder, $v=330c{{m}^{3}}$ .

We have been told that the length of the cylinder is 4cm. which we can take as the height of the cylinder, as shown in the figure. We can take the height as ‘h’.
Therefore, the height of the cylinder, $h=4cm$ .
We need to find the radius of the cylinder is we need to find ‘r’, we know the volume of a cylinder is given by the formula, volume of cylinder $=\pi \times {{\left( \text{radius} \right)}^{2}}\times \text{height}$ .
i.e. $v=\pi {{r}^{2}}h$ .
We know the value of $v=330c{{m}^{{}}}$ and $h=4cm$ . take $\pi =\dfrac{22}{7}$ .
\[\begin{align}
  & \therefore v=\pi {{r}^{2}}h \\
 & 330=\pi {{r}^{2}}\times 4 \\
 & \Rightarrow {{r}^{2}} = \dfrac{330}{\pi \times 4}=\dfrac{330}{\dfrac{22}{7}\times 4}=\dfrac{330\times 7}{22\times 4}=\dfrac{30\times 7}{2\times 4}=\dfrac{15\times 7}{8} \\
 & {{r}^{2}}=\dfrac{105}{8},\text{ now take square} \\
 & \therefore \text{r=}\sqrt{\dfrac{105}{8}}=5.12cm \\
\end{align}\]
Hence we got the radius of the cylinder as 5.12cm
$\therefore $ Option (C) is the correct answer.

Note: This is one of the easier question to solve. We have been given v and h and it is a direct substitution of a variable into the formula for finding the volume. Don’t forget to take the root of ${{r}^{2}}$ to obtain the radius of the base of the cylinder.