Question

height of a right circular cone is double of height of a cylinder find the ratio of there volume if they have equal radius​

Answer 1

Given:-

• Height of a right circular cone is double of height of a cylinder.
• Both right circular cone and cylinder have same radius.

To find:-

Ratio of Volume of right circular cone and cylinder.

Assumption:-

Let the volume of right circular cone be $\sf{V_1}$ and volume of cylinder be $\sf{V_2}$.

Let the height of cylinder be x

height of right-circular cone = 2x

Solution:-

We know,

$\sf{Volume\:of\:Right\:circular\:cone = 4\pi r^2 \dfrac{h}{3}}$

Therefore,

$\sf{V_1 = 4\pi r^2 \dfrac{2x}{3}}$

= $\sf{V_1 = \dfrac{8x \pi r^2}{3}}$

Now,

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

= $\sf{V_2 = \pi r^2 x}$

= $\sf{V_2 = 2x \pi r^2}$

Now,

Ratio of volume of Right circular cone and cylinder:-

= $\sf{V_1 : V_2 = \bigg(\dfrac{8x\pi r^2}{3}\bigg) : (2x \pi r^2)}$

= $\sf{\dfrac{V_1}{V_2} = \dfrac{\dfrac{8x\pi r^2}{3}}{2x\pi r^2}}$

= $\sf{\dfrac{V_1}{V_2} = \dfrac{8x \pi r^2}{3} \times \dfrac{1}{2x\pi r^2}}$

= $\sf{\dfrac{V_1}{V_2} = \dfrac{4}{3}}$

Therefore,

$\sf{V_1 : V_2 = 4:3}$

Ratio of volumes of cylinder and right circular cone is 4 : 3.

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Formulas to be kept in mind:-

• Volume of right circular cone = $\sf{4\pi r^2 \dfrac{h}{3}\:\:cu.units}$

• Curved Surface Area (CSA) of right circular cone = $\sf{\pi r l\:\:sq.units}$

• Total Surface Area (TSA) of a right circular cone = $\sf{\pi r (r+l)\:\:sq.units}$

• Volume of Cylinder = $\sf{\pi r^2 h\:\:units}$

• Total Surface Area of Cylinder = $\sf{2\pi r(r+h)\:\:sq.units}$

• Curved Surface Area of cylinder = $\sf{2\pi rh\:\:sq.units}$

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Answer 2

$\huge{\boxed{\rm{\red{Question}}}}$

Height of a right circular cone is double of height of a cylinder . Find the ratio of there volume if they have equal radius .

$\huge{\boxed{\rm{\red{Answer}}}}$

${\bigstar}\large{\boxed{\sf{Given \: that}}}$

• Height of a right circular cone is double of height of a cylinder.
• The radius of both circular cone and cylinder have same radius.

${\bigstar}\large{\boxed{\sf{To \: find}}}$

• Radius of volume of right circular cone and cylinder.

${\bigstar}\large{\boxed{\sf{Let's}}}$

• The volume of right circular cone will be V¹ and the volume of cylinder will be V²
• Height of cylinder will be x
• Height of right circular cone will be 2x

${\bigstar}\large{\boxed{\sf{Solution}}}$

• Radius of volume of right circular cone and cylinder = 4:3

${\bigstar}\large{\boxed{\boxed{\underline{\sf{4:3 \: is \: the \: answer}}}}}$

${\bigstar}\large{\boxed{\sf{Full \: solution}}}$

As we know that,

Formula of volume of right circular cone –

• vπr²h/3

So now let's carry on

• V¹ = 4πr² 2x/3
• V¹ = 8xπr²

Now,

Formula of volume of cylinder –

• πr²h

So now let's carry on

• V² = 2xπr²

Now,

Let's ratio of volume of right circular cone and cylinder –

• V¹ : V²
• 8xπr² / 3 : 2xπr²
• v¹ / v² = 8xπr² / 3 / 2xπr²
• v¹ / v² = 8xπr² / 3 × 1 / 2xπr²

{By cancelling xπr² by xπr² the result is 0 }

• v¹ / v² = 4/3

We know that the question is in ratio.

So we have to find the result in ratio.

• v¹ : v² = 4:3

Therefore, 4:3 is the answer.

@Itzbeautyqueen23

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