Question

) The area of the base of the cylinder is 44sq.cm and volume are 440cubic cm.

Find the height of the cylinder.​

Answer 1

GIVEN :-

The area of the base of the cylinder = 44cm²

Volume of cylinder = 440cm³

TO FIND:

Height of the cylinder

$\underline{\bigstar{\sf{ \ SOLUTION:-}}}$

We know that, the base of cylinder is a circle.

$\boxed{\sf {\dag\ \ Area \ of\ circle = \pi r^2= 44 cm}}$

Find the radius of cylinder

$\longrightarrow\sf \pi r^2= 44\\ \\ \longrightarrow\sf \dfrac{22}{7}\times r^2= 44\\ \\ \longrightarrow\sf r^2= \cancel{44}\times \dfrac{7}{\cancel{22}}\\ \\ \longrightarrow\sf r^2= 14 \\ \\ \longrightarrow\sf r= \sqrt{14}\\ \\ \longrightarrow\sf r= 3.74cm$

Radius of circular base of cylinder = 3.74cm

Now, let's find the height of the cylinder

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

$\longrightarrow\sf \pi r^2 h= 440\\ \\ \longrightarrow\sf \dfrac{22}{7}\times (3.74)^2 \times h = 440\\ \\ \longrightarrow\sf 14.01 \times h = \cancel{440}\times \dfrac{7}{\cancel{22}}\\ \\ \longrightarrow\sf 14.01 \times h = 20 \times 7 \\ \\ \longrightarrow\sf 14.01 \times h = 140\\ \\ \sf\ \ \ let's\ assume \ 14.01 \ as\ 14cm\\ \\ \longrightarrow\sf h = \cancel{\dfrac{140}{14}}\\ \\\longrightarrow\sf h = 10cm$

$\boxed{\sf{\therefore\ \ the\ height\ of \ cylinder\ is\ 10cm}}$

Answer 2

$\huge\sf\red{Answer:}$

☆ Given:

⇒ The area of the base of the cylinder is 44sq.cm and volume are 440cubic cm.

☆ Find:

⇒ Find the height of the cylinder.

☆ According to the question:

⇒ We know that the base of a cylinder is 'Circle' so let's use this formula 'Area of circle'. Let us assume 'R' as radius and 'H' be height. Note that the value of pi is 22/7.

☆ Using formula:

⇒ $\sf Area \: of \: circle = πr^2 = 44\: cm$

☆ Calculations:

⇒ $\sf πr^2 = 44$

⇒ $\sf \dfrac{22}{7} \times R^2= 44$

⇒ $\sf R^2 = 44 \times \dfrac{7}{22}$

⇒ $\sf R^2 = 14$

⇒ $\sf R = \sqrt{14}$

⇒ ${\sf{\underline{\boxed{\green{\sf{3.74 \: cm}}}}}}$

Therefore, 3.74 cm is the radius of circular base of cylinder.

But according to the question, we have to find the height of the cylinder. Using the above equations we can find the height of the cylinder.

☆ Using formula:

⇒ $\sf Volume \: of \: cylinder = πr^2h$

☆ Calculations:

⇒ $\sf πr^2 h = 440$

⇒ $\sf \dfrac{22}{7} \times (3.74)^2 \times H = 440$

⇒ $\sf 14.01 \times H$

⇒ $\sf 440 \times \dfrac{7}{22}$

⇒ $\sf 14.01 \times H$

⇒ $\sf 20 \times 7$

⇒ $\sf 14.01 \times H$

⇒ ${\sf{\underline{\boxed{\green{\sf{140}}}}}}$

⇒ $\sf H = \dfrac{140}{14}$

⇒ ${\sf{\underline{\boxed{\green{\sf{H = 10 \: cm}}}}}}$

Therefore, 10 cm is the height of cylinder.