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# Ex.13.4 Q2 Surface Areas and Volumes Solution - NCERT Maths Class 9

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## Question

Find the surface area of a sphere of diameter:

i. $$14 \, \rm cm$$

ii. $$21 \, \rm cm$$

iii. $$3.5 \, \rm m$$

Video Solution
Surface-Areas-And-Volumes
Ex exercise-13-4 | Question 2

## Text Solution

Reasoning:

Surface area of the sphere of radius $$r$$ is equal $$4$$ times the area of the circle of radius $$r.$$

\begin{align}S = 4\pi {r^2} \end{align}

What is known?

Diameter of the sphere.

What is unknown?

Surface area of the sphere.

Steps:

(i)  Diameter ( $$2r$$ ) $$= 14{\rm\,{ cm}}$$

Radius ($$r$$) $$= 7\,\rm\,{cm}$$

Surface area

\begin{align}&= 4\pi {r^2}\\ & = 4 \times \frac{{22}}{7} \times 7 \times 7\\&= 616\,\rm{cm^2} \end{align}

(ii) Diameter($$2 r$$) = $$21 \rm\,{cm}$$

Radius ($$r$$) = $${\frac{21}{2} \, \mathrm {cm}}$$

Surface area

\begin{align}&={4 \times \frac{22}{7} \times \frac{21}{2} \times \frac{21}{2}} \\&={1386 \, \mathrm{cm}^{2}}\end{align}

(iii) Diameter ($$2 r$$$$= 3.5\rm\, m$$

Radius ($$r$$) $$= \frac{3.5}{2}\rm\, m$$

Surface area

\begin{align} &={4 \times \frac{22}{7} \times \frac{3.5}{2} \times \frac{3.5}{2}} \\ &={38.5 \mathrm{m}^{2}}\end{align}

\begin{align}&\text{(i) 616} \rm\,{cm^2}\\&\text{(ii) 1386}\rm\,{cm^2}\\&\text{(iii) 38.5}\,\rm\,{m^2} \end{align}