Ex.13.4 Q6 Surface Areas and Volumes Solution - NCERT Maths Class 9

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Question

Find the radius of a sphere whose surface area is \(154\,\rm\,{m^2}.\)

Text Solution

Reasoning:

The surface area of the sphere is equal to \(4\) times the surface area of the circle if \(r\) is the sphere and circle. \(S = 4\pi {r^2} \)

What is known?

Surface area of the sphere.

What is unknown?

Radius of the sphere.

Steps:

Surface area of the sphere \(= 4\pi {r^2}\)

\[\begin{align} 154 &= 4 \times \frac{{22}}{7} \times {r^2}\\{r^2} &= \frac{{154}}{4} \times \frac{7}{{22}}\\{r^2} &= 7 \times 7 \times \frac{1}{2} \times \frac{1}{2}\\r\, &= 7 \times \frac{1}{2}\\&= 3.5\,\rm{cm} \end{align}\]

Answer:

Radius of the sphere \(= 3.5 \, \rm cm\)