Question

A solid cylinder has a total surface area of 231cm². Its curved surface area is 2/3 of the total surface area. Find the volume of the cylinder.​

Answer 1

Answer:

Step-by-step explanation:

Let the radius of the cylinder be r and the height be h

The curved surface area of the cylinder is given by

2pierh

Total surface area of the solid cylinder is given as the sum of the curved surface area and the areas of the base and the top: 2πr$r^{2}$ +2πrh

Given that  2πrh= 2/3 (2πrh+2π$r^{2}$)

⇒h=2r

Also, given that

2π$r^{2}$ +2πrh=231

6πr ^2 =231

r= $\sqrt{\frac{77}{2pie} }$

Volume of the cylinder:

=πr ^2 h

volume = 77$\sqrt{\frac{77}{2pie} }$