Question

Two cubes have their volume in the ratio 8:27 the ratio of their surface areaa is:​

Answer 1

Answer:

24:54

Step-by-step explanation:

Given: areas are in ratio 8:27

$area = {side}^{3} \\ side = \sqrt[3]{area}$

$hence \\ sides \: are \: in \: ratio \\ \sqrt[3]{8 } : \sqrt[3]{27} = 2 : 3$

$surface \: area = 6 \times {side}^{2}$

$therefore \: ratio \: of \: surface \\ areas \: is \\ 6 \times {2}^{2} : 6 \times {3}^{2}$

$= 6 \times 4 : 6 \times 9 \\ =24 :54$

Answer 2

Two cubes have their volume in the ratio 8:27 the ratio of their surface area is 4 : 9

Solution:

Let the Sides of cube be a, b

The volume of cube is given as:

$volume = side^3$

For a cube with side length "a"

$volume = a^3$

For a cube with side length "b"

$volume = b^3$

Given that, Two cubes have their volume in the ratio 8 : 27

Therefore,

$a^3 : b^3 = 8 : 27\\\\\frac{a^3}{b^3} = \frac{8}{27}\\\\(\frac{a}{b})^3 = (\frac{2}{3})^3\\\\ Powers\ are\ same\ therefore\\\\\frac{a}{b} = \frac{2}{3}$

Therefore,

a = 2

b = 3

Find the surface area :

Surface area of cube = $6(side)^2$

For a cube with side length "a" = 2

Surface area of cube = $6(2)^2 = 6 \times 4 = 24$

For a cube with side length "b" = 3

Surface area of cube = $6(3)^2 = 6 \times 9 = 54$

Find the ratio

Ratio = 24 : 54

Reduce to lowest term

Ratio = 4 : 9

Thus, the ratio of their surface area is 4 : 9

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