The radius of cone is increased by 25% and height is decreased by 20%, then percentage change in volume is (a) 20% (b) 12.5% (c) 37.5 % (d) None of above
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Answers
Answer:
20 percent
Step-by-step explanation:
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None of these ☑️
Original volume of a cone = [\piπ r²h]÷3
Given that,
Radius is increased by 25%
Height is decreased by 20%
New Volume = \piπ ×[r25/100)×r}]²×[h-(20/100)×h
= \piπ ×(5r/4)²×(4h/5)
= \piπ ×(25r²/16)×(4h/5)
= \piπ ×5r²/4×h
= [5\piπ r²h]÷4
Change in Volume = [(5\piπ r²h)÷4] - [(\piπ r²h)÷3]
= [15\piπ r²h - 4\piπ r²h]÷12
= [11\piπ r²h]÷12
Percentage change = [(11\piπ r²h/12)÷(\piπ r²h/3)]×100
= 275% INCREASE
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