Question

Find the total surface area and volume of a hemisphere, whose radius is 7 cm .​

Answer 1

$\huge\mathfrak{\red{Answer}}$

• Total Surface area is 462 cm^2

• Volume is 718.7 cm^3

Step-by-step explanation:

$\huge\underline\mathcal{\red{Question:-}}$

$\implies$ Find the total surface area and volume of a hemisphere, whose radius is 7 cm .

$\huge\underline{\overline{\mid{\bold{\purple{\mathbb{Hint:-}}\mid}}}}$

$\Rightarrow$ We will first use the formula for the total Surface area of the hemisphere.

$\Rightarrow$ Then, We will find the Volume of the hemisphere by using the formula of the volume of the hemisphere.

$\huge\underline{\overline{\mid{\bold{\blue{\mathtt{Formulas:-}}\mid}}}}$

Related to Hemisphere:

• Curved surface area $\implies$ 2πr^2

• Total Surface area $\implies$ 3πr^2

• Volume $\implies$ 2/3 πr^3

$\huge\underline{\overline{\mid{\bold{\green{\mathfrak{Solution:-}}\mid}}}}$

For Total Surface area:-

Given, Radius of the hemisphere, r = 7cm.

We know that;

Total Surface area of the hemisphere is given by 3πr^2

Putting values we have

$= 3 \times \pi \times 7 \times 7$

$= 3 \times \frac{22}{7} \times 7 \times 7$

$= 3 \times 22 \times 7$

$= 66 \times 7$

$= 462 \: {cm}^{2}$

Total Surface area is 462cm^2

___________________________________________________

For Volume:-

Given, Radius of the hemisphere, r = 7cm.

We know that;

Volume of the hemisphere is given by 2/3 πr^3

Putting values we have

$= \frac{2}{3} \times \pi \times 7 \times 7 \times 7$

$= \frac{2}{3} \times \frac{22}{7} \times 7 \times 7 \times 7$

$= \frac{2}{3} \times 22 \times 49$

$= \frac{2}{3} \times 1078$

$= 718.7 \: {cm}^{3} (approx.)$

Volume is 718.7 cm^3

$\tiny\mathfrak{\red{ \ \ \ \ \ @MissTranquil}}$

Answer 2

Given : The Radius of Hemisphere is 7 cm .

Exigency To Find : Total Surface Area and Volume of Hemisphere.

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❍ Finding Total Surface Area of Hemisphere :

$\dag\frak{\underline {As,\;We\;Know \:that\::}}$

$\dag\:\boxed {\sf{Total \:Surface\:Area\:_{(Hemisphere)} = \bigg( 3\pi r^2 \bigg) }}$

Where,

• r is the Radius of Hemisphere
• $\pi =\dfrac{22}{7}$

⠀⠀⠀⠀⠀⠀$\underline {\frak{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$:\implies \sf{ T.S.A \: = 3 \times \pi \times 7^2 }\\\\:\implies \sf{ T.S.A \: = 3 \times \pi \times 7 \times 7 }\\\\:\implies \sf{ T.S.A \: = 3 \times \dfrac{22}{\cancel {7}} \times \cancel {7} \times 7 }\\\\:\implies \sf{ T.S.A \: = 3 \times 22 \times 7 }\\\\:\implies \sf{ T.S.A \: = 66 \times 7 }\\\\\underline {\boxed{\pink{ \mathrm {  T.S.A \: = 462\: cm^2}}}}\:\bf{\bigstar}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Hence,\:Total \:Surface \:Area \:of\:Hemisphere \:is\:\bf{462\: cm^2}}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Finding Volume of Hemisphere :

$\dag\frak{\underline {As,\;We\;Know \:that\::}}$

$\dag\:\boxed {\sf{Volume \:_{(Hemisphere)} = \bigg( \dfrac{2}{3}\pi r^3 \bigg) }}$

Where,

• r is the Radius of Hemisphere
• $\pi =\dfrac{22}{7}$

⠀⠀⠀⠀⠀⠀$\underline {\frak{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$:\implies \sf{ Volume = \dfrac {2}{3} \times \pi \times 7^3 }\\\\ :\implies \sf{ Volume = \dfrac {2}{3} \times \pi \times 7 \times 7 \times 7 }\\\\:\implies \sf{ Volume = \dfrac {2}{3} \times \dfrac{22}{\cancel {7}} \times \cancel {7} \times 7 \times 7 }\\\\:\implies \sf{ Volume = \dfrac {2}{3} \times 22 \times 7 \times 7 }\\\\ :\implies \sf{ Volume = \dfrac {2}{3} \times 22 \times 49 }\\\\:\implies \sf{ Volume = \dfrac {2}{\cancel {3}} \times \cancel {1078} }\\\\:\implies \sf{ Volume = 2 \times 359.33.. }\\\\\underline {\boxed{\pink{ \mathrm {  Volume = 718.66\: cm^{3}\qquad (Approx)}}}}\:\bf{\bigstar}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Hence,\:Volume \:of\:Hemisphere \:is\:\bf{718.66\: cm^3\qquad(Approx)}}}}$

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