Question

The radius of a cylinder is 7 cm and its height is 16 cm. Find
i) Total surface area of the cylinder
ii) volume of the cylinder
-2​

Answer 1

$\large \bf{ \underline{ \underline{Answer :}}}$

• Total surface area of the cylinder is 1012 cm².

• Volume of the cylinder is 2464 cm³.

Elucidation:

Here, it's given that radius of the cylinder is 7 cm and height of the cylinder is 16 cm. And we are asked to calculate the :-

• Total surface area of the cylinder

• Volume of the cylinder

Firstly, we'll be calculating the total surface area of the cylinder, by applying this formula :

• $\boxed{ \rm{ \rm{ \gray{2 \pi \: r(h + r)}}}}$

And lastly we'll be calculating the volume of the cylinder, by applying this formula :

• $\boxed{ \rm{ \gray{\pi \: r ^2 h }}}$

Given:

• Radius = 7 cm
• Height = 16 cm

To Find:

1. Total surface area of the cylinder
2. Volume of the cylinder

Calculation:

~ Calculating the total surface area of cylinder,

To calculate the total surface area of the cylinder, we'll be using this formula :-

• $\boxed{ \bf{ \red{2 \pi \: r(h + r)}}}$

$\dag$ Putting the values,

$\sf {\longrightarrow {TSA}_{(Cylinder)} = 2\pi \: r(h + r)} \\ \\ \\ \sf {\longrightarrow {TSA}_{(Cylinder)} = 2 \times \dfrac{22}{7} \times 7 \: (7 + 16)} \\ \\ \\ {\longrightarrow \sf {TSA}_{(Cylinder)} = 2 \times \dfrac{22}{7} \times 7 \: \times 23} \\ \\ \\ {\longrightarrow \sf {TSA}_{(Cylinder)} = 44 \: \times 23} \\ \\ \\ \longrightarrow \boxed{\sf { {TSA}_{(Cylinder)} = 1012 \: {cm}^{2} }} \: { \pink \bigstar}$

Therefore, total surface area of the cylinder is 1012 cm².

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~ Calculating the volume of the cylinder,

To calculate the volume of the cylinder, we'll be using this formula :-

• $\boxed{ \bf{ \red{\pi \: r ^2 h }}}$

$\dag$ Putting the values,

$\sf {\longrightarrow {Volume}_{(Cylinder)} = \pi \: r^2 h } \\ \\ \\ \sf {\longrightarrow {Volume}_{(Cylinder)} = \dfrac{22}{7} \times 7 \times 7 \times 16 } \\ \\ \\ \sf {\longrightarrow {Volume}_{(Cylinder)} = 22 \times 7 \times 16 } \\ \\ \\ \longrightarrow \boxed{\sf { {Volume}_{(Cylinder)} = 2464 \: {cm}^{3} }} \: { \blue \bigstar}$

Therefore, volume of the cylinder is 2464 cm³.

Answer 2

Given

• Radius of cylinder = 7 cm
• Height of cylinder = 16 cm

To find

• Total surface area of cylinder
• Volume of cylinder

Solution

• T.S.A = 2πr(r + h)
• T.S.A = 2 × 22/7 × 7(7 + 16)
• T.S.A = 44/7 × 7(23)
• T.S.A = 44/7 × 161
• T.S.A = 1012

Hence, the total surface area is 1012 cm².

• Volume = πr²h
• Volume = 22/7 × 7 × 7 × 16
• Volume = 22/7 × 49 × 16
• Volume = 154 × 16
• Volume = 2464

Hence, the volume of cylinder is 2464 cm³.