Question

The radius and height of a cylinder are in the ratio 4:7.Find the diameter of the cylinder if it's volume is 1188cm³.

Answer 1

Given: Ratio of radius & height of the cylinder i.e 4:7 & volume of the cylinder is 1188cm³.

Need to find: Diameter of the cylinder ?

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❍ Let's consider the base and height of the cylinder be 4x cm and 7x cm.

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As we know that,

$\begin{gathered}\star\:{\underline{\boxed{\frak{Volume_{\:(Cylinder)} = \pi \times r^{2} \times h}}}}\\\\\\ \bf{\dag}\:{\underline{\frak{Putting\:given\:values\:in\:formula,}}}\\\\\\ :\implies\sf \dfrac{22}{7}\times {4x}^{2} \times 7x = 1188\\\\\\ :\implies\sf 22 \times 16{x}^{3} = 1188\\\\\\ :\implies\sf 352{x}^{3} = 1188\\\\\\ :\implies\sf x^3 = \cancel{\dfrac{1188}{352}}\\\\\\ :\implies\sf x^3 = 3.375\\\\\\ :\implies\sf \sqrt{x^3} = \sqrt{3.375} \\\\\\ :\implies{\underline{\boxed{\frak{\purple{x = 1.5}}}}}\:\bigstar\\\\\end{gathered}$

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Therefore,

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• Radius of the cylinder = 4x = 6cm

• Height of the cylinder = 7x = 10.5cm

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$\therefore\:{\underline{\sf{Hence,\: diameter\:of\:the\: cylinder\:is\:\bf{1.5\:cm}\: \sf{respectively}.}}}$

Answer 2

★ Given :

• The radius and height of a cylinder are in the ratio 4:7. Volume is 1188cm³.

★ To find :

• Diameter of the circle

★ Solution :

• Let radius = 4x

• And height = 7x

• Volume = 1188cm³

✪ In the question It is given to find the Diameter Of the Cylinder. Let the Radius be 4x and The height be 7x.

✪ We know the formula of Volume of Cylinder. Then Putting The value in the volume We will find The Value of x.

✪ The put the values in 4x and 7x we will get radius and Height. The double of the radius is diameter.

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✾ Now Let's solve ✾

Volume of cylinder = πr²h

➤ 1188cm³ = 22/7 × (4x)³ × 7x

➤ 1188cm³ = 22 × 16x³

➤ x³ = 1188/22

➤ x³ = 3.375

➤ x = 1.5

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➛Radius = 4x = 6cm

➛Height = 7x = 10.5 cm

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∴ Diameter Of Cylinder is 1.5 cm.