Question
If the radius of a sphere is increased by 50%, find the increase percent in volume and the increase percent in he surface area .
Answer: Option D
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Let original radius = R. , Then new radius = `150/100 R = (3R)/(2)`
Original volume =` 4/3 pi R^3,` New volume = `4/3 pi ((3R)/(2))^3 = (9 pi R^3)/(2)`
Increase % in volume = `(19/6 piR^3 xx (3)/(4 pi R^3) xx 100)%` = 237.5%
Original surface area = `4piR^2`
New surface area = `4pi ((3R)/(2))^2 = 9 pi R^2`
Increase % in surface area = `((5 pi R^2)/(4 pi R^2) xx 100)`% = 125%
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