Question

find the volume and the total surface area of a right circular solid cylinder whose radius and height respectively are 7 cm and 30 cm .​

Answer 1

Given:

• Radius of cylinder = 7 cm
• Height of cylinder = 30 cm

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To Find:

• Volume and total surface area.

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Solution:

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Here In the question we are given radius of cylinder 7 cm and height of cylinder 30 cm. So, we can easily find the volume of cylinder.

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Using formula:

$~~~~ \underline{ \boxed{ \sf{ \pmb{Volume \: of \: cylinder = \pi {r}^{2} h}}}} \: \pink\bigstar$

$\longrightarrow \sf \frac{22}{7} \times {(7)}^{2} \times 30 \\ \\ \\ \longrightarrow \sf \dfrac{22}{ \cancel{7}} \times \cancel{7} \times 7 \times 30 \\ \\ \\ \longrightarrow \sf22 \times 7 \times 30\\ \\ \\ \longrightarrow \sf154 \times 30 \\ \\ \\ \longrightarrow\underline { \boxed { \sf{ \pmb {4620 {cm}^{3} }}}} \: \pink \bigstar$

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Hence, the required volume of cylinder is 4620 cm³. Now, we will find the total surface area of the right circular cylinder.

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${ \underline{ \boxed{ \sf{ \pmb{TSA \: of \: cylinder = 2\pi r(r + h)}}}}} \: \pink \bigstar$

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$\longrightarrow \sf </p><p>2 \times \dfrac{22}{ \cancel{7}} \times \cancel{7}(7 + 30) \\ \\ \\ \longrightarrow\sf 44(7 + 30) \\ \\ \\ \longrightarrow \sf 44 \times 37 \\ \\ \\ \longrightarrow { \underline{ \boxed{ \sf{ \pmb{1628 {cm}^{2} }}}}} \:\pink \bigstar$

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H E N C E,

• Volume of cylinder = 4620 cm³
• TSA of cylinder = 1628 cm ²

Answer 2

✮ Given :-

Radius of Cylinder = > 7 cm

Height of Cylinder = > 30 cm

✰ To Find :-

Volume of Cylinder :-

Total Surface Area of Cylinder :-

✮ Formula used here :-

Volume of Cylinder = > πr²h

Total Surface area of Cylinder => 2πr(r+h)

✰ Solution Start :-

$Volume \: of \: Cylinder = > πr²h \\ \\ Volume \: of \: Cylinder \: = > \frac{22}{7} \times 7 \times 7 \times 30 \\ \\ Volume \: of \: Cylinder = > \frac{22}{\cancel {7}} \times \cancel {7} \times \times 7 \times 30 \\ \\ Volume \: of \: Cylinder \: = > 22 \times 7 \times 30 \\ \\ Volume \: of \: Cylinder \: = > 154 \times 30 \\ \\ Volume \: of \: Cylinder = > \:4620 \: {cm}^{3}$

✰ Hence, Volume of Cylinder = > 4620 cm³

$Total \: Surface \: area \: of \: Cylinder => 2πr(r+h) \\ \\ Total \: Surface \: area \: of \: Cylinder => 2 \times \frac{22}{7} \times 7(7 + 30) \\ \\ Total \: Surface \: area \: of \: Cylinder =>2 \times \frac{22}{\cancel {7}} \times \cancel {7}(37) \\ \\ Total \: Surface \: area \: of \: Cylinder => 44 \times 37 \\ \\ Total \: Surface \: area \: of \: Cylinder => 1628 \: {cm}^{2}$

✰ Hence,Total Surface area of Cylinder => 1628 cm²

Hope it's helpful for you !!!