Question

The curved surface area of a cylinder is 1210 cm² and it's diameter is 20 cm. Find it's height and volume.

Answer 1

ANSWER:-

Given:

The curved surface area of a cylinder is 1210cm².

It's diameter is 20cm.

To find:

Find it's height & volume.

Solution:

We know that, curved surface area of a cylinder;

=) 2πrh

⚫Radius= 20/2 = 10cm

Now,

$= > 2 \times \frac{22}{7} \times 10 \times h = 1210 \\ \\ = > \frac{44}{7} \times 10 \times h = 1210 \\ \\ = > h = \frac{1210 \times 7}{44 \times 10} \\ \\ = > h = \frac{77}{4} cm$

Therefore,

Volume of a cylinder is πr²h.

$= > \frac{22}{7} \times 10 \times 10 \times \frac{77}{4} \\ \\ = > \frac{22}{7} \times 100 \times \frac{77}{4} \\ \\ = >( 22 \times 25 \times 11) {cm}^{3} \\ \\ = > 6050 {cm}^{3}$

Thus,

⚫Height of a cylinder is 77/4cm

⚫Volume of a cylinder is 6050cm³.

Hope it helps ☺️

Answer 2

$\bf{\underline{\underline \blue{Solution:-}}}$

$\sf\underline{\red{\:\:\: AnswEr:-\:\:\:}}$

• The height of cylinder = 19.25 Cm
• The volume of cylinder = 6050 Cm³

$\sf\underline{\red{\:\:\: Given:-\:\:\:}}$

• The curved surface area of a cylinder is 1210 cm² and it's diameter is 20 cm.

$\sf\underline{\red{\:\:\: Need\:To\: Find:-\:\:\:}}$

• The height of cylinder = ?
• The volume of cylinder = ?

$\bf{\underline{\underline \blue{Explanation:-}}}$

$\sf\underline{\red{\:\:\: We\:know\: that:-\:\:\:}}$

$\bigstar \: \boxed{ \sf \: Radius = \frac{Diameter}{2} }$

$\sf\underline{\orange{\:\:\: Putting\:the\: values:-\:\:\:}}$

$\dashrightarrow \sf {Radius = \dfrac{\cancel{20}}{\cancel{2}}\:}$

$\dashrightarrow \sf {Radius = 10\:Cm}$

$\rule{200}{2}$

$\dag$ In First Situation:

$\sf\underline{\green{\:\:\: Need\:To\: Find:-\:\:\:}}$

• The height of cylinder = ?

$\sf\underline{\red{\:\:\: Formula\:used\: here:-\:\:\:}}$

$\bigstar \: \boxed{ \sf \: Curved \:surface\: area\: of \:a \:cylinder = 2\pi rh }$

$\sf\underline{\red{\:\:\: Now,Putting\:the\: values:-\:\:\:}}$

$\dashrightarrow \sf {2 \times \frac{22}{7} \times 10 \times Height = 1210}$

$\dashrightarrow \sf {\frac{44}{7} \times 10 \times Height = 1210}$

$\dashrightarrow \sf {Height = 1210 \times \frac{7}{440} }$

$\dashrightarrow \sf {Height = \dfrac{\cancel{8470}}{\cancel{440}}\ }$

$\dashrightarrow \sf {Height = 19.25\:Cm}$

$\sf\underline{\green{\:\:\: ThereFore:-\:\:\:}}$

• The height of cylinder is 19.25 Cm.

$\rule{200}{2}$

$\dag$ In Second Situation:

$\sf\underline{\green{\:\:\: Need\:To\: Find:-\:\:\:}}$

• The volume of cylinder = ?

$\sf\underline{\red{\:\:\: Formula\:used\: here:-\:\:\:}}$

$\bigstar \: \boxed{ \sf \: Volume\:of \:a \:cylinder = \pi r^2h }$

$\sf\underline{\red{\:\:\: Now,Putting\:the\: values:-\:\:\:}}$

$\dashrightarrow \sf {Volume = \frac{22}{7} \times 10 \times 10 \times 19.25}$

$\dashrightarrow \sf {Volume = \frac{2200 \times 19.25}{7} }$

$\dashrightarrow \sf {Volume = \dfrac{\cancel{42350}}{\cancel{7}}\ }$

$\dashrightarrow \sf {Volume = 6050\:Cm^3}$

$\sf\underline{\green{\:\:\: ThereFore:-\:\:\:}}$

• The volume of cylinder is 6050 Cm³.

$\rule{200}{2}$