Question

5. Ratio of surface areas of two cubes is 1 : 4. Find
the ratio of their sides.​

Answer 1

Given:-

Ratio of surface areas of two cubes = 1:4

To find:-

Ratio of their sides.

Assumption:-

Let the side of 1st cube be a

Let the side of 2nd cube be b

Solution:-

Surface Area of 1st cube = 6a²

Surface Area of 2nd cube = 6b²

Therefore,

Surface Area of 1st cube:Surface Area of 2nd cube = 1:4

= $\sf{6a^2:6b^2 = 1:4}$

=> $\sf{\dfrac{6a^2}{6b^2} = \dfrac{1}{4}}$

=> $\sf{\dfrac{a^2}{b^2}= \dfrac{1}{4}}$

=>$\sf{\dfrac{a}{b}= \sqrt{\dfrac{1}{4}}}$

=> $\sf{\dfrac{a}{b} =\dfrac{1}{2}}$

=> a:b = 1:2

Therefore ratios of the side of cube is 1:2

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More Informations:-

• Volume of a cube = (side)³ cu.units

• Total Surface Area of the cube = 6a² sq.units.

• Lateral Surface Area of the cube = 4a² sq.units.

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