Find the surface area of a sphere of diameter:
Question. Find the surface area of a sphere of diameter:

(i) $14 \mathrm{~cm}$

(ii) $21 \mathrm{~cm}$

(iii) $3.5 \mathrm{~m}$

[Assume $\left.\pi=\frac{22}{7}\right]$


Solution:

(i) Radius $(r)$ of sphere $=\frac{\text { Diameter }}{2}=\left(\frac{14}{2}\right) \mathrm{cm}=7 \mathrm{~cm}$

Surface area of sphere $=4 \pi r^{2}$

$=\left(4 \times \frac{22}{7} \times(7)^{2}\right) \mathrm{cm}^{2}$

$=(88 \times 7) \mathrm{cm}^{2}$

$=616 \mathrm{~cm}^{2}$

Therefore, the surface area of a sphere having diameter $14 \mathrm{~cm}$ is $616 \mathrm{~cm}^{2}$.

(ii) Radius $(r)$ of sphere $=\frac{21}{2}=10.5 \mathrm{~cm}$

Surface area of sphere $=4 \pi r^{2}$

$=\left[4 \times \frac{22}{7} \times(10.5)^{2}\right] \mathrm{cm}^{2}$

$=1386 \mathrm{~cm}^{2}$

Therefore, the surface area of a sphere having diameter $21 \mathrm{~cm}$ is $1386 \mathrm{~cm}^{2}$.

(iii) Radius $(r)$ of sphere $=\frac{3.5}{2}=1.75 \mathrm{~m}$

Surface area of sphere $=4 \pi r^{2}$

$=\left[4 \times \frac{22}{7} \times(1.75)^{2}\right] \mathrm{m}^{2}$

$=38.5 \mathrm{~m}^{2}$

Therefore, the surface area of the sphere having diameter $3.5 \mathrm{~m}$ is $38.5 \mathrm{~m}^{2}$.
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