# The Ratio Between the Radius of the Base and the Height of a Cylinder is 2 : 3. Find the Total Surface Area of the Cylinder, It Its Volume is 1617 Cm3. - Mathematics

Sum

The ratio between the radius of the base and the height of a cylinder is 2 : 3. find the total surface area of the cylinder, it its volume is 1617 cm3.

#### Solution

Data given is as follows:

r/h = 2/3

Volume = 1617 cm3

We have to find the Total surface area

From the given data, we have

r/h = 2/3

Therefore, h = 3/2r

Also, we know that

Volume = pir^2h=1617

pir^2h =1617

xx 22/7 xx r xx r3/2 xx r =1617

r^3 = 343

r =7 cm

h = 3/2 xx7

h = 21/2 cm

Therefore, total surface area is

TSA = 2 pir( r +h)

⇒ TSA = 2 xx 22/7 xx 7 (7 +21/2)

⇒ TSA = 770  cm^2

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 12 | Page 21

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