If the Radii of Two Cylinder Are in the Ratio 2 : 3 and Their Heights Are in the Ratio 5 : 3, Then Find the Ratio of Their Volumes. - Mathematics

Short Note

If the radii of two cylinder are in the ratio 2 : 3 and their heights are in the ratio 5 : 3, then find the ratio of their volumes.

Solution

Let r1 and r2 be the radii of the two cylinders respectively and h1 and h2 are the heights of the two cylinders respectively. It is given that r_1 : r_2 = 2:3 and h_1 : h_2 = 5:3

We are asked to find the ratio of the volumes of the two cylinders

Now;

"Volume of cylinder 1 "/"Volume of cylinder 2" = (pir_1^2h_1)/(pir_2^2 h^2)

=(r_1/r_2)^2(h_1/h_2)

=(2/3)^2(5/3)

= 20/27

Therefore the ratio of the volumes of the tw2o cylinders is  20 : 27

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 19.3 | Q 4 | Page 28

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