Question

Two cylinder of same volume have their radius in the ratio 1:6. Find the ratio of their heights.​

Answer 1

hope it helps

refer to the attachment

Answer 2

Given :

• Volume of two cylinder are equal
• Radius of two cylinder are in ratio 1:6

To find :

Ratio of height

Formula used :

Volume of cylinder = π r² h

Solution :

For 1st cylinder

Volume = V₁

Radius = r₁

Height = h₁

Therefore,

Volume ( V₁ ) = π (r₁ )² h₁

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For 2nd cylinder

Volume = V₂

Radius = r₂

Height = h₂

Therefore,

Volume ( V₂ ) = π (r₂)² h₂

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Now , we know that volume of both are equal

Therefore,

V₁ = V₂

$\sf \implies \: \not{\pi} \: \times (r_1)^2 \times h_1 \:=\: \not{\pi} \times (r_2)^2 \times h_2 \\ \\ \sf \implies \: \dfrac{h_1}{ h_2} \: = \: \dfrac{(r_2)^2}{(r_1)^2} \\ \\ \sf \implies \: \dfrac{h_1}{ h_2} \: = \: \bigg( \dfrac{r_2}{r_1} \bigg)^{2} \: \: \: \: \: \: .....equation1$

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As we are given that

$\sf r_1 \: : \: r _2 = 1 : 6 \\\\\sf \implies \: \dfrac{r_1}{r_2} \:=\: \dfrac{1}{6}\\\\\sf \implies \: \dfrac{r_2}{r_1} \:=\: \dfrac{6}{1}$

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On putting value of ( r₂ ÷ r₁ ) in equation 1 , we get;

$\sf \implies \: \dfrac{h_1}{ h_2} \: = \: \bigg( \dfrac{6}{1} \bigg)^{2} \\ \\ \sf \implies \: \dfrac{h_1}{ h_2} \: = \dfrac{36}{1} \\ \\ \sf \implies \: h_1 \: : \: h_2 \: = \: 36\: : \:1$

ANSWER :

Ratio of height = 36 : 1