Question

The area of the base of a right circular cylinder is 154 \[{{\operatorname{cm}}^{2}}\] and its height is 15 cm, find the volume of the cylinder.

Answer 1

Hint:Assume the radius of the base of the right circular cylinder as r. We know that the area of circular base is \[\pi {{r}^{2}}\] .We have the area of circular base that is, 154 \[{{\operatorname{cm}}^{2}}\] . Get the radius of the circular base. We know that the volume of the cylinder is \[\pi {{r}^{2}}h\] . Put the values of height and radius and then solve it further.

Complete step-by-step answer:
Let the radius of the base of the right circular cylinder be r.
The area of circular base = \[\pi {{r}^{2}}\] ………………….(1)
According to the question it is given that the area of the circular base is 154 \[{{\operatorname{cm}}^{2}}\] and the height of the cylinder is 15 cm.
\[\begin{align}
  & \pi {{r}^{2}}=154 \\
 & \Rightarrow \dfrac{22}{7}\times {{r}^{2}}=154 \\
 & \Rightarrow {{r}^{2}}=\dfrac{154\times 7}{22} \\
 & \Rightarrow {{r}^{2}}=7\times 7 \\
 & \Rightarrow r=7 \\
\end{align}\]
So, the radius of the circular base is 7 cm.
We know that the volume of the cylinder is \[\pi {{r}^{2}}h\] .
Radius = 7 cm ,
Height = 15 cm .
Putting the values of radius and height in the formula \[\pi {{r}^{2}}h\] , we get
\[\begin{align}
  & \pi {{r}^{2}}h \\
 & =\dfrac{22}{7}\times 7\times 7\times 15 \\
 & =22\times 7\times 7 \\
 & =154\times 15 \\
 & =2310 \\
\end{align}\]
Hence, the volume of the cylinder is 2310 \[c{{m}^{3}}\] .

Note: We can also solve this question without finding the value of radius.
We know that the area of circular base is \[\pi {{r}^{2}}\] and it is given that area of circular base is 154 \[{{\operatorname{cm}}^{2}}\] .
\[\pi {{r}^{2}}=154\] …………………..(1)
Volume of cylinder = \[\pi {{r}^{2}}h\] …………….(2)
From equation (1) and equation (2), we have
Volume of cylinder = \[\pi {{r}^{2}}h=154h\] ………………………..(3)
Putting the value of height in equation (3), we get
Volume of cylinder = \[154h=154\times 15=2310c{{m}^{3}}\] .
Hence, the volume of the cylinder is 2310 \[c{{m}^{3}}\] .