Question

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Easy Question :-
The radius and height of a cylinder are in the ratio 5:7 and it volume is 550cm cube. Find the radius and surface area of the cylinder

Answer 1

Given :-

• The radius and height of a cylinder are in the ratio 5:7  

• It’s volume is  550 cm.

To Find :-

• Find the radius and surface area of the cylinder

Solution :-

~Here, we’re given the ratio of radius and height of cylinder and the volume. We need to find the radius and surface area of the cylinder. Firstly we’ll find the radius and height by putting the values in the formula of volume of cylinder and then find the surface area.

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According to the given ratios :-  

• The Radius be ‘5x’  

• The height be ‘7x’

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As we know that ,

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

$\underline{\boxed{\sf \bigstar \;\; Surface\;area\;of\;cylinder = 2 \pi r (h + r) }}$

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Finding the radius and height ::

$\sf \implies 550 = \dfrac{22}{7} \times 5x \times 5x \times 7x$

$\sf \implies 550 = 22 \times 5x \times 5x \times x$

 

$\sf \implies 550 = 550x^{3}$

$\sf \implies x^{3} = \dfrac{550}{550}$

 

$\sf \implies x^{3} = 1$

$\sf \implies x = \sqrt[3]{1}$

$\boxed{\sf{\star \;\; x=1}}$

Therefore,  

$\sf \leadsto height = 7\;cm$

$\sf \leadsto radius = 5\;cm$

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Finding the Surface area ::  

$\sf \implies 2 \times \dfrac{22}{7} \times 5 ( 5 + 7 )$

$\sf \implies 2 \times \dfrac{22}{7} \times 5 \times 12$

$\boxed{\sf{\star \;\; 376.8 \;cm^{2}}}$

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Hence,  

• The radius is 5 cm and the surface area is 376.8 cm  

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Answer 2

Given:-

☞ The radius and height of a cylinder are in the ratio 5:7 and it volume is 550cm cube.

To Find:-

☞ The Radius and Surface of the Area of the Cylinder When Hight and Volume is Given.

Solution:-

➵ Let the radius of the base and height of the cylinder be 5x cm and 7x cm respectively.

Then,

$➠ \: Volume = 550 {cm}^{3}$

$➠ \: \frac{22}{7} (5 {x}^{2} ) \times 7x = 550$

$➠ \: 22 \times 25 {x}^{3} = 550$

$➠ \: x = 1cm$

➵ Hence ,radius of the cylinder = 5x = 5 cm.