Question

If surface area of a sphere is 784πcm2 .Find its radius.​

Answer 1

Given:

• Surface area of sphere = 784 π cm²

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To find:

• Radius of sphere?

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Sphere is a ball shape where the surface is the same distance from the center at all points.

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⌬ Let radius of sphere be r cm.

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We know that,

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$\star\;{\boxed{\sf{\purple{TSA_{\;(sphere)} = 4 \pi r^2}}}}$

Now, Putting values,

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$:\implies\sf 4 \cancel{\pi} r^2 = 784 \cancel{ \pi}$

$:\implies\sf 4 \times r^2 = 784$

$:\implies\sf r^2 = 784 \times \dfrac{1}{4}$

$:\implies\sf r^2 = 196$

$:\implies\sf \sqrt{r^2} = \sqrt{196}$

$:\implies{\boxed{\sf{\pink{r = 14\;cm}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;Radius\;of\;sphere\;is\; \bf{14\;cm}.}}}$

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$\qquad\qquad\boxed{\underline{\underline{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}$

• TSA of hemisphere = 3πr²

• CSA of hemisphere = 2πr²

• Volume of sphere = 4/3 πr³

• Volume of hemisphere = 2/3 πr³

Answer 2

Given ,

The surface area of sphere is 784π cm²

We know that , the surface area of sphere is given by

$\boxed{ \tt{Area = 4\pi {(r)}^{2} }}$

Thus ,

784π = 4π × (r)²

196 = (r)²

r = ± √196

r = ± 14 cm

Since , the length can't be negative

Therefore , the radius of sphere is 14 cm

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