InterviewSolution
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Radius of a right circular cone is decreased by 20%. To maintain the same volume, the height will have to be increased by?1). 20%2). 40.75%3). 44%4). 56.25% |
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Answer» ⇒ Let radius be R, height be h and VOLUME be V ⇒ Then initial volume of cone is ⇒ V = (1/3) × (π × r2 × h) ⇒ Now if radius is DECREASED by 20% then new radius will be = r – 20% of r ⇒ New radius = 0.8r ⇒ Suppose new height INCREASED by x % ⇒ Then new height = h + x% of h ⇒ New height = (100h + x × h)/100 ⇒ New height = (h/100) × (100 + x) ⇒ New volume = (1/3) × (π × 0.8r2 × (h/100) × (100 + x) ⇒ As volume remains the same so ratio of volume will be same ⇒ (Initial volume)/(New Volume) = 1 ----- 1 ⇒ Putting the value of each in 1 we get ⇒ {(1/3) × (π × r2 × h) }/{(1/3) × (π × 0.8r2 × (h/100) × (100 + x) } = 1 ⇒ 100/(0.64) × (100 + x) = 1 ∴ x = 56.25% |
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