If the radius of a sphere is tripled, then its surface area increased by
If the radius of a sphere is tripled, then its surface area increased by
1). 150%
2). 300%
3). 600%
4). 800%
1 answers
Surface area of sphere with radius r is given by,
Surface area = 4πr2 sq. units
When the radius of the sphere triples, the new radius becomes r1 = 3r
∴ new surface area of sphere = 4π × (3r)2 = 36πr2 sq. units
$(\therefore \;\% \;increase\;in\;area\; = \frac{{new\;area - original\;area}}{{original\;area}} \times 100)$
$(\Rightarrow \% \;increase\;in\;area\; = \frac{{36\;\pi {r^2} - 4\;\pi {r^2}}}{{4\;\pi {r^2}}} \times 100 = 800)$
∴ Surface area of a sphere increases by 800% when its radius triples.Other Questions
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