Question

if base diameter of a cylinder is increased by 50%, then by how much percent its height must be decreased so as to keep its volume unaltered?
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Answer 1

Answer:

hey mate,

Step-by-step explanation:

Let r be the radius and h be the height of the cylinder.

∴ Original volume, V = πr²h

(i) Radius is increased by 50%:

New radius, r₁ = r - 50% of r

= r - (50/100) * r

= r - r/2

= r/2.

(ii) Height increased by 50%:

New height, h₁ = h + 50% of h

= h + (50/100) * h

= h + h/2

= 3h/2

∴ New volume, V₁ = πr₁²h₁

= π(r/2)²(3h/2)

= (3/8)πr²h

Decrease in volume = V - V₁

= (1 - 3/8π)r²h

= (5/8)πr²h

%Decrease in volume = [5/8πr²h/πr²h] * 100%

= [5/8] * 100%

= 62.5%.

Therefore, decrease in volume = 62.5%

thank you