Question

The radius of sphere is
3.5cm: Find its surface
area and volume.
​

Answer 1

Given: Radius of sphere = 3.5 cm

Need to find: Surface Area and Volume of sphere.

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$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Total\;surface\;area_{\;(sphere)} = 4 \pi r^2}}}}$

$:\implies\sf TSA_{\;(sphere)} = 4 \times \dfrac{22}{ \cancel{7}} \times \cancel{3.5} \times 3.5$

$:\implies\sf TSA_{\;(sphere)} = 4 \times 22 \times 0.5 \times 3.5$

$:\implies\sf TSA_{\;(sphere)} = 4 \times 22 \times 1.75$

$:\implies{\underline{\boxed{\frak{\purple{TSA_{\;(sphere)} = 154\;cm^2}}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Total\;surface\;area\;of\;sphere\;is\; \bf{154\;cm^2}.}}}$

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$\star\;{\boxed{\sf{\pink{Volume_{\;(sphere)} = \dfrac{4}{3} \pi r^3}}}}$

$:\implies\sf Volume_{\;(sphere)} = \dfrac{4}{3} \times \dfrac{22}{7} \times (3.5)^3$

$:\implies\sf Volume_{\;(sphere)} = \dfrac{4}{3} \times \dfrac{22}{ \cancel{7}} \times \cancel{42.875}$

$:\implies\sf Volume_{\;(sphere)} = \dfrac{4}{3} \times 22 \times 6.125$

$:\implies\sf Volume_{\;(sphere)} = \dfrac{88}{3} \times 6.125$

$:\implies{\underline{\boxed{\frak{\purple{Volume_{\;(sphere)} = 179.66\;cm^3}}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Volume\;of\;sphere\;is\; \bf{179.66\;cm^3}.}}}$

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

• Total surface area of hemisphere = 3πr²

• Curved surface area of hemisphere = 2πr²

• Volume of hemisphere = 4/3 πr³

Answer 2

Answer:

Given :-

• The radius of a sphere is 3.5 cm.

To Find :-

• What is the surface area and volume.

Formula Used :-

❶ To find surface area we know that,

$\boxed{\bold{\large{T.S.A\: of\: Sphere\: =\: 4{\pi}{r}^{2}}}}$

❷ To find volume we know that,

$\boxed{\bold{\large{Volume\: of\: Sphere\: =\: \dfrac{4}{3}{\pi}{r}^{3}}}}$

Solution :-

Radius of a sphere is 3.5 cm.

❶ First, we have to find the T.S.A of sphere,

⇒ T.S.A of sphere = $4\: \times \dfrac{22}{7} \times {(3.5)}^{2}$

⇒ T.S.A of sphere = $4\: \times \dfrac{22}{7} \times 3.5 \times 3.5$

⇒ T.S.A of sphere = $4\: \times \dfrac{22}{7} \times 12.25$

⇒ T.S.A of sphere = $\dfrac{1078}{7}$

⇒ T.S.A of sphere = $\sf\dfrac{\cancel{1078}}{\cancel{7}}$

➠ T.S.A of sphere = 154 cm²

Hence, the total surface area of sphere is 154 cm² .

❷ Now, we have to find the volume of sphere,

⇒ Volume of sphere = $\dfrac{4}{3} \times \dfrac{22}{7} \times {(3.5)}^{3}$

⇒ Volume of sphere = $\dfrac{4}{3} \times \dfrac{22}{7} \times 3.5 \times 3.5 \times 3.5$

⇒ Volume of sphere = $\dfrac{4}{3} \times \dfrac{22}{7} \times 42.875$

⇒ Volume of sphere = $\dfrac{3773}{21}$

⇒ Volume of sphere = $\sf\dfrac{\cancel{3773}}{\cancel{21}}$

➠ Volume of sphere = 179.67 cm³

Hence, the volume of sphere is 179.67 cm³ .