Question:
The surface area of a sphere is 2464 cm2. If its radius be doubled, then what will be the surface area of the new sphere?
Solution:
Let the radii of the given sphere and the new sphere be r and R, respectively.
We have,
$R=2 r$ and the surface area of the given sphere $=2464 \mathrm{~cm}^{2}$
i.e. $4 \pi r^{2}=2464 \mathrm{~cm}^{2}$
The surface area of the new sphere $=4 \pi R^{2}$
$=4 \pi(2 r)^{2}$
$=4 \pi\left(4 r^{2}\right)$
$=4\left(4 \pi r^{2}\right)$
$=4 \times 2464$
$=9856 \mathrm{~cm}^{2}$
So, the surface area of the new sphere is 9856 cm2.
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