Question

9. Ratio of surface areas of two cubes is 1:25. Find the ratio of their volumes.​

Answer 1

$\huge \mathscr{\orange {\underline{\pink{\underline {Answer:-}}}}}$

Since,

● The surface area of cubes is given by 6a² where 'a' is the length of each side of the cube .

So,

● According to the question let the side length of one cube be 'x ' and side length of other cube be 'y'.

● According to  question ratio of surface area is 1:25

⇒ 6x² /6y² = 1:25

⇒ x/y = 1/5

● Now we have to find ratio of volumes 

● Volume of a cube is x³ where 'x' is the length of the side of cube .

∴Ratio of volumes both the cubes is x³ /y³ 

= (1/5)³

⇒ 1/125.

Answer 2

Given:-

• Ratio of surface areas of two cubes is 1:25.

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To find:-

• The ratio of their volumes.

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Solution:-

Let,

• the edges of the two respective cubes be x and y.

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$\tt\longmapsto{\dfrac{6x^2}{6y^2} = \dfrac{1}{25}}$

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$\tt\longmapsto{\bigg\lgroup{\dfrac{x}{y}\bigg\rgroup^2 = \bigg\lgroup{\dfrac{1}{5}\bigg\rgroup^2}}}$

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$\tt\longmapsto{\bigg\lgroup{\dfrac{x}{y} = \dfrac{1}{5} \bigg\rgroup}}$

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• Volume

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$\tt\longmapsto{\dfrac{4^3}{4^3} = \bigg\lgroup{\dfrac{1}{5} \bigg\rgroup^3}}$

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$\tt\longmapsto{\bigg\lgroup{\dfrac{x}{y}\bigg\rgroup^3 = \bigg\lgroup{\dfrac{1}{2}\bigg\rgroup^3}}}$

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$\tt\longmapsto{\dfrac{1}{125}}$

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$\tt\longmapsto{\boxed{\orange{1:125}}}$

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Hence,

• the ratio of their volumes is 1:125.