# A Solid Cylinder Has a Total Surface Area of 231 Cm2. Its Curved Surface Area is 2 3 of the Total Surface Area. Find the Volume of the Cylinder. - Mathematics

Sum

A solid cylinder has a total surface area of 231 cm2. Its curved surface area is $\frac{2}{3}$ of the total surface area. Find the volume of the cylinder.

#### Solution

We know that the total surface area of the cylinder is 231 cm2 and the curved surface area is 2/3 of the total surface area.
So, the curved surface area is:
2/3 x (231 cm2) = 154 cm2
Then, the radius of the cylinder can be calculated in the following manner:
Curved surface area = 2πrh
​154 cm2 = 2πrh         ... (1)
Here, r  cm is the radius of the cylinder and h cm is the length of the cylinder.
2πr2 = (231-154) cm2 = 77 cm2
77 cm2 = 2π​r2
From here, the radius (r) can be calculated in the following manner:

$r = \sqrt{\frac{77}{2 \times \frac{22}{7}}}$
r = 3.5 cm
Substituting this result into equation (1):
154 cm2 = 2π(3.5 cm)h
h= 154 cm2 / (2x 22/7x (3.5cm))
h = 7 cm
∴ V = π​r2h = $\frac{22}{7}$x (3.5 cm)2 x (7 cm) = 269.5 cm3
Hence, the volume of the cylinder is 269.5 cm3.
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 22 Mensuration - III (Surface Area and Volume of a Right Circular Cylinder)
Exercise 22.2 | Q 36 | Page 26