Question

If the diameter of cylinder inceases by 20% and height decreases by 20%. by what will the volume increase

Answer 1

The original volume of a cylinder
V = πr2h

The new volume of a cylinder
V1 = πR2H

Now, if the diameter of the cylinder increases by 20%,
D = d + ( d x 20 ) / 100
D = d x 120 / 100
But 2xR = D
2 x R = 2 x (r x 120) / 100
R = r x 120 / 100
R2= (r x 120)2 / 1002
R2= r2 x 14400 / 10000


And if the height decreases by 20%
H = h - ( h x 20 ) / 100
H = h x 80 / 100

Now V1 becomes,
V1 = π(R)2(H)
V1 = π x (r2 x 14400 / 10000) x (h x 80 / 100)
V1 = π x r2 x h x (14400 x 80 / 10000 x 100)
But, πr2h = V
V1 = V x (144 x 8 / 1000)
V1 = V x 1.152

So, the increased volume will be 1.152 times the original volume