If the base radius and the height of a right circular cone are increased by 20%, then the percentage increase in volume is approximately
A. 60
B. 68
C. 73
D. 78
Answers
Given : Let the base radius of a cone be 'r' and the height of a cone be 'h'.
Volume of cone = ⅓ πr²h
New radius of a cone = r + 20% of r
= r + 20/100 × r
= r + r/5
= (5r + r)/5
New radius of a cone = 6r/5
New height of a cone = h + 20% of h
= h + 20/100 × h
= h + h/5
= (5h + h)/5
New height of a cone = 6h/5
New volume = ⅓ × π × (6r/5)² × 6h/5
New volume = ⅓ × π × 36r/25 × 6h/5
New volume = ⅓ π × 216r²h/125
Increase in volume = ⅓ π × 216r²h/125 - ⅓ πr²h
= 1/3π (216r²h/125 - r²h)
= ⅓π (216r²h - 125r²h)/125
Increase in volume = ⅓π (91r²h)/125
Percentage increase in volume =
(⅓π (91r²h)/125)/ ⅓ πr²h × 100
= (91)/125) × 100
= 9100/125
= 72.8%
= Approx 73%
Option (C) 73% is correct.
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