How much percent of the curved surface area of a sphere will be increased if the radius is doubled?
WBBSE
Class X
Mathematics
Sphere
02 Mark
2024
Curved surface area (C.S.A) of a sphere = 4πr²
If radius is doubled
⇒ new radius = 2r.
New C.S.A = 4π(2r)² = 4π × 4r² = 16πr².
Increase in C.S.A = (New C.S.A − Old C.S.A)
= 16πr² − 4πr² = 12πr²
% increase = (Increase C.S.A / Old C.S.A) × 100
= (12πr² / 4πr²) × 100
= 300%.
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