# 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

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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.

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#### Solution

Given data is as follows:

Total Surface Area = 231 cm2

Curved Surface Area = 2/3 ("Total Surface Area" )

We have to find the volume of the cylinder.

We have,

Total Surface Area = 231 cm2

2pirh+ 2pir^2=231

Where, 2pirh  is nothing but the Curved Surface Area.

Curved Surface Area = 2/3 ("Total Surface Area" )

Curved Surface Area= 2/3 xx 231 =154

Let us replace 2pirh  in the above equation with the value of Curved Surface Area we have just obtained.

154+2pir^2 =231

2pir^2 =77

2 xx 22/7 xx r^2=77

r^2 = (77 xx 7)/(2 xx 22 ) = (7xx7)/(2xx2)

r = 7/2

Now, let us find the value of  h by using the Curved Surface Area.

Curved Surface Area=154 cm2

2pirh =154

Since we know that  r = 7/2 ,

2 xx 22/7 xx 7/2 xx h =154

h = 7

Now that we know the value of both h and r , we can easily find the volume of the cylinder.

Volume of the cylinder =  pir^2h

=22/7 xx 7/2xx7/2xx7

"Volume of the cylinder "= 269.5cm^3

Concept: Surface Area of Cylinder
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 19 Surface Areas and Volume of a Circular Cylinder
Exercise 19.2 | Q 26 | Page 22

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