Question

The radius and height of a cylinder are in the ratio 3:4 and it's volume is 38808cm find it's radius and height​

Answer 1

Given :

The radius and height of a cylinder are in the ratio 3:4 and it's volume is 38808cm .

To find :

It's radius and height.

Solution :

Let the radius and height be 3y cm and 4y ​

cm respectively.

As we know,

Volume of cylinder = πr²h

⇒ 38808 = 22/7 * (3y)² * 4y

⇒ 38808 = 22/7 * 9y² * 4y

⇒ 38808 * 7/22 = 36y³

⇒ 12348 = 36y³

⇒ y³ = 12348/36

⇒ y³ = 343

⇒ y = ∛343

⇒ y = 7

∴ Radius of cylinder = 3y = 3 * 7 = 21 cm

∴ Height of cylinder = 4y = 4 * 7 = 28 cm

Therefore,

Radius and height are 21 cm and 28 cm respectively.

Answer 2

Answer:

✯ Given :-

• The radius and height of a cylinder are in the ratio of 3:4 and it's volume is 38808 cm.

✯ To Find :-

• What is the radius and height of a cylinder.

✯ Formula Used :-

$\boxed{\bold{\small{❖ Volume\: of\: Cylinder\: = πr²h}}}$

✯ Solution :-

» Let, the radius be 3x and height be 4x

➣ According to the question by using the formula we get,

⇒ 38808 = $\dfrac{22}{7}$ × (3x)² × 4x

⇒ 38808 = $\dfrac{22}{7}$ × 36x³

⇒ 36x³ = $\dfrac{38808 × 7}{22}$

⇒ 36x³ = $\dfrac{271656}{22}$

⇒ 36x³ = $\sf\dfrac{\cancel{271656}}{\cancel{22}}$

⇒ 36x³ = 12348

⇒ x³ = $\sf\dfrac{\cancel{12348}}{\cancel{36}}$

⇒ x³ = 343

⇒ x = $\sqrt[3]{343}$

⇒ x = $\sqrt[3]{(7)³}$

➥ x = 7 cm

Hence,

◪ Radius of a cylinder = 3x = 3(7) = 21 cm

◩ Height of a cylinder = 4x = 4(7) = 28 cm

$\therefore$ The radius of a cylinder is 21 cm and the height of a cylinder is 28 cm .

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