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Ex.13.4 Q1 Surface Areas and Volumes Solution - NCERT Maths Class 9

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Question

Assume \(\pi = \frac{{22}}{7} \) unless stated otherwise

Find the surface area of a sphere of radius:

(i) \(10.5 \rm \, cm \)

(ii) \(5.6 \rm \, cm\)

(iii) \(14 \rm \, cm \)

 Video Solution
Surface-Areas-And-Volumes
Ex exercise-13-4 | Question 1

Text Solution

Reasoning:

Surface area of sphere of radius \(r\) \(= 4\pi\,\rm{r^2}\) 

What is known?

Radius of the sphere.

What is unknown?

Surface area of the sphere

Steps:

(i) Radius \(= 10. 5\rm\, cm\)

Surface area of the sphere

\[\begin{align}&= 4\pi {r^2}\\&= 4 \times \frac{{22}}{7} \times {(10.5)^2} \\&= 1386\,\rm{cm^2} \end{align}\]

(ii) Radius \(= 5.6\rm\, cm\)

Surface area of the sphere

\[\begin{align} &= 4\pi {r^2}\\&= 4 \times \frac{{22}}{7} \times {(5.6)^2}\\ &= 394.24\,\rm{cm^2} \end{align}\]

(iii) Radius \(= 14\rm\, cm\)

Surface area of the sphere

\[\begin{align} &= 4\pi {r^2} \\&= 4 \times \frac{{22}}{7} \times {(14)^2}\\ &= 2464\,\rm{cm^2} \end{align}\]

Surface area

\(\begin{align}&\text{(i) 1386}\,\rm{cm^2}\\&\text{(ii) 394.24}\,\rm{cm^2}\\&\text{(iii) 2464}\,\rm{cm^2} \end{align}\)