Question

$\huge\underbrace\mathbb{Question}$

The radius of the base of a right circular cylinder is halved and the height is doubled. What is the ratio of the volume of the new cylinder to that of the original one.

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Answer 1

Step-by-step explanation:

Let the radius and height of the cylinder be r and h respectively.

Volume of the cylinder = π×r²×h

Now, According to question,

New radius = r/2 , New height = 2h

New Volume = π ×(r/2)² × 2h = π × r²/4 × 2h = π×r²×h/2

= 0.5 π×r²×h

Ratio of volumes = (0.5πr²h)/πr²h = 0.5 = 1/2 = 1:2

Answer 2

Hola mate your answer below⚡⚡

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${\huge{\bold{\underline{given}}}}$

• A right circular cylinder
• Radius = halfed
• height = doubled

${\huge{\bold{\underline{to\: find}}}}$

• ratio of the volume of the new cylinder to that of the original one.

${\huge{\bold{\underline{explanation}}}}$

Original cylinder :

Radius = r

Height = h

volume = πr²h

$\implies$22/7 x r x r x h

New cylinder

Radius = r /2

Height = 2 h

volume = πr²h

$\implies$22/7 x r/2 x r/2 x h

hence, ratio =

New cylinder / original cylinder

22/7 x r/2 x r/2 x h //22/7 x r x r x h

{ cancel out 22/7}{h}{r}

hence the required ratio is

1 : 2

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