Question

The radius of the base of a closed cylinder is 7 cm and height is 10cm.find.1) Area of its base .2) total surface area.3) volume of cylinder.4) curved surface area.answer the following ( 4 marks each)
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Answer 1

Answer:

⠀⠀⠀⌬ Radius = 7 cm

⠀⠀⠀⌬ Height = 10 cm

⠀

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1. Area of it's Base

$:\implies\sf Area_{Base}=\pi r^2\\\\\\:\implies\sf Area_{Base}= \dfrac{22}{7} \times (7)^2\\\\\\:\implies\sf Area_{Base} = 22 \times 7\\\\\\:\implies\sf Area_{Base} = 154 \:cm^{2}$

$\rule{200}{1}$

2. Total Surface Area

$:\implies\sf TSA=CSA+2 \times Base\:Area\\\\\\:\implies\sf TSA=2\pi rh+2 \times 154\\\\\\:\implies\sf TSA = \bigg(2 \times \dfrac{22}{7} \times 7 \times 10 \bigg) + 308\\\\\\:\implies\sf TSA = (2 \times 22 \times 10) + 308\\\\\\:\implies\sf TSA = 440 + 308\\\\\\:\implies\sf TSA = 748 \:cm^{2}$

$\rule{200}{1}$

3. Volume of cylinder

$:\implies\sf Volume=Base\:Area \times Height\\\\\\:\implies\sf Volume = 154 \:{cm}^{2} \times 10 \:cm\\\\\\:\implies\sf Volume = 1540\: {cm}^{3}$

$\rule{200}{1}$

4. Curved Surface Area

$:\implies\sf CSA=2\pi rh\\\\\\:\implies\sf CSA=\bigg(2 \times \dfrac{22}{7} \times 7 \times 10 \bigg)\\\\\\:\implies\sf CSA = 2 \times 22 \times 10\\\\\\:\implies\sf CSA = 440 \: {cm}^{2}$

Answer 2

Step-by-step explanation:

1. Area of it's Base

\begin{gathered}:\implies\sf Area_{Base}=\pi r^2\\\\\\:\implies\sf Area_{Base}= \dfrac{22}{7} \times (7)^2\\\\\\:\implies\sf Area_{Base} = 22 \times 7\\\\\\:\implies\sf Area_{Base} = 154 \:cm^{2} \end{gathered}

:⟹Area

Base

=πr

2

:⟹Area

Base

=

7

22

×(7)

2

:⟹Area

Base

=22×7

:⟹Area

Base

=154cm

2

\rule{200}{1}

2. Total Surface Area

\begin{gathered}:\implies\sf TSA=CSA+2 \times Base\:Area\\\\\\:\implies\sf TSA=2\pi rh+2 \times 154\\\\\\:\implies\sf TSA = \bigg(2 \times \dfrac{22}{7} \times 7 \times 10 \bigg) + 308\\\\\\:\implies\sf TSA = (2 \times 22 \times 10) + 308\\\\\\:\implies\sf TSA = 440 + 308\\\\\\:\implies\sf TSA = 748 \:cm^{2} \end{gathered}

:⟹TSA=CSA+2×BaseArea

:⟹TSA=2πrh+2×154

:⟹TSA=(2×

7

22

×7×10)+308

:⟹TSA=(2×22×10)+308

:⟹TSA=440+308

:⟹TSA=748cm

2

\rule{200}{1}

3. Volume of cylinder

\begin{gathered}:\implies\sf Volume=Base\:Area \times Height\\\\\\:\implies\sf Volume = 154 \:{cm}^{2} \times 10 \:cm\\\\\\:\implies\sf Volume = 1540\: {cm}^{3} \end{gathered}

:⟹Volume=BaseArea×Height

:⟹Volume=154cm

2

×10cm

:⟹Volume=1540cm

3

\rule{200}{1}

4. Curved Surface Area

\begin{gathered}:\implies\sf CSA=2\pi rh\\\\\\:\implies\sf CSA=\bigg(2 \times \dfrac{22}{7} \times 7 \times 10 \bigg)\\\\\\:\implies\sf CSA = 2 \times 22 \times 10\\\\\\:\implies\sf CSA = 440 \: {cm}^{2} \end{gathered}

:⟹CSA=2πrh

:⟹CSA=(2×

7

22

×7×10)

⟹CSA=2×22×10

⟹CSA=440cm

2

Hope it helps

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