Question

the csa of a right circular cylinder is 396 cm^2 . the area of cross section is 154 cm^2 . what is the volume of the cylinder ?​

Answer 1

Given :

• CSA of cylinder = 396 cm².
• Area of cross section = 154 cm².

To find :

• Volume of the cylinder.

Solution :

Consider ,

• Radius of the cylinder = r cm
• Height of the cylinder = h cm

According to the 1st condition :-

• CSA of cylinder = 396 cm².

$\implies\sf{2\pi\:r\:h=396..............(1)}$

According to the 2nd condition :-

• Area of cross section = 154 cm².

$\implies\sf{\pi\:r^2=154}$

$\implies\sf{\dfrac{22}{7}\times\:r^2=154}$

$\implies\sf{r^2=154\times\dfrac{7}{22}}$

$\implies\sf{r^2=49}$

$\implies\sf{r=7}$

• Radius= 7 cm.

Now , put r = 7 in eq (1) .

$\implies\sf{2\pi\:r\:h=396}$

$\implies\sf{2\times\dfrac{22}{7}\times\:7\times\:h=396}$

$\implies\sf{h=396\times\dfrac{1}{2}\times\dfrac{7}{22}\times\dfrac{1}{7}}$

$\implies\sf{h=9}$

• Height= 9 cm

$\implies\sf{Volume=\pi\:r^2h}$

$\implies\sf{Volume=\dfrac{22}{7}\times\:7\times\:7\times\:9\:cm^3}$

$\implies\sf{Volume=22\times\:7\times\:9\:cm^3}$

$\implies\sf{Volume=1386\:cm^3}$

Therefore, the volume of the cylinder is 1386 cm³.