# The Ratio Between the Curved Surface Area and the Total Surface Area of a Right Circular Cylinder is 1 : 2. Find the Volume of the Cylinder, If Its Total Surface Area is 616 Cm2. - Mathematics

Sum

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Find the volume of the cylinder, if its total surface area is 616 cm2.

#### Solution

Data given is as follows:

"Curved Surface Area"/("Total Surface Area")=(1/2)

"Total Surface Area = 616 cm"^2

We have to find the volume of the cylinder.

From the given data we have,

"Curved Surface Area"/"Total Surface Area" = (1/2)

"Curved Surface Area "= (1/2) xx "Total Surface Area "

 =(1/2) xx 616  cm^2

 = 308  cm^2

Also,

"Curved Surface Area"/"Total Surface Area " = (1/2)

(2pirh)/(2pirh + 2 pi r^2) = 1/2

h/(h+r)=1/2

2h = h + r

h = r

We have found out the Curved Surface Area of the cylinder which is 308 cm2

Curved Surface Area = 308 cm2

2pirh =308

Now, let us replace h with r in the above equation since in the previous step we have found that  h = r .

2pir^2 =308

2 xx 22/7 xx r^2 = 308

r = 7

Since h = r , h is also equal to 7

Volume = pi r^2 h

=22/7 xx 7 xx 7 xx 7

Volume = 1078 cm3

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 10 | Page 21

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