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Q.


A right angled triangle whose sides are3 cm, 4 cm and 5 cmrevolved about the sides containing the right angle in two ways. Find the difference in volumes of the two cones so formed.

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a

4π cm3

b

4π cm3

c

4π cm3

d

4π cm3 

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Detailed Solution

Given,
The sides of right angle = 3, 4, and 5 cm
Here, hypotenuse side is 5 cm (longest side).
So, sides containing right angles are 3 cm and 4 cm.
Now, the triangle is revolve around 3 cm and 4 cm. Here, we get two cones of this revolution with 3 cm radius and 4 cm radius with height 4 cm and 3 cm respectively.
Thus, the volumes,
V1=13π324 
V1=12π 
Also,
V2=13π42(3)
V2=16π
Thus, difference in the volume,
ΔV=π16-12
ΔV=4π cm3
Hence, option 2 is correct.
 
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A right angled triangle whose sides are3 cm, 4 cm and 5 cmrevolved about the sides containing the right angle in two ways. Find the difference in volumes of the two cones so formed.