Question

the ratio of the radii of a two cylinder of same height is 1ratio 3. If the volume of first cylinder is 50cm2 then find the volume of second cylinder​

Answer 1

S O L U T I O N :

Given,

• The ratio of the radii of a two cylinders is 1 : 3.
• Height is same.
• Volume of first cylinder = 50 cm³

To Find,

• The volume of second cylinder.

Explanation,

We know that,

Volume of cylinder = πr²h

[ For first cylinder ]

• Volume (V1) = 50 cm³
• Radius (r1) = 1r
• Height is same.

[ For second cylinder ]

• Volume (V2) = ?
• Radius (r2) = 3r
• Height is same.

We ask to find, "The volume of second cylinder".

V1 / V2 = π(r1)²h / π(r2)²h

=> 50/V2 = π × (1r)²× h / π × (3r)² × h

=> 50/V2 = πr²h / π9r²h

=> 50/V2 = 1/9

=> V2 = 50 × 9

=> V2 = 450 cm³

Therefore,

The volume of second cylinder is 450 cm³.

Answer 2

Given

• The ratio of the radii of a two cylinder of same height is 1:3.
• Volume of first cylinder is 50 cm³.

⠀

To find

• Volume of second cylinder.

⠀

Solution

• Let the radius be r.

⠀

⠀⠀⠀❍ Radius of first cylinder = 1r

⠀⠀⠀❍ Radius of second cylinder = 3r

⠀

• Since, the height of both cylinder is equal.

⠀

Formula used

⠀

$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt{\bigstar{Volume_{(Cylinder)} = \pi r^2h{\bigstar}}}}$

⠀

→ $\sf{Let\: the\: volume\: of\: second\: Cylinder\: be\: V_2}$

⠀

According to the question

$\tt\longmapsto{\dfrac{V_1}{V_2} = \dfrac{\pi r^2h}{\pi r^2h}}$

⠀

$\tt\longmapsto{\dfrac{50}{V_2} = \dfrac{\cancel{\pi} \times (1r)^2 \times \cancel{h}}{\cancel{\pi} \times (3r)^2 \times \cancel{h}}}$

⠀

$\tt\longmapsto{\dfrac{50}{V_2} = \dfrac{1\cancel{r^2}}{9\cancel{r^2}}}$

⠀

$\tt\longmapsto{\dfrac{50}{V_2} = \dfrac{1}{9}}$

⠀

$\tt\longmapsto{V_2 = 50 \times 9}$

⠀

$\bf\longmapsto{V_2 = 450}$

⠀

Hence,

• The volume of second cylinder is 450 cm³.

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