Question

If the ratio of volumes of cube is 8:27 then ratio of total surface areas is

Answer 1

ratio of volume = r^3/R^3

8/27=r^3/R^3

r/R=2/3

Total surface area ratio=6×r^2/6×R^2

=r^2/R^2

=4/9

the ratio of surface area of cube is in ratio 4:9

Answer 2

Answer:

Total surface area of cube is 4:9

Step-by-step explanation:

Explanation:

Given , the ratio of volumes of cube is 8 :27 .

Let x be the side of the first cube and y be the side of the second cube

Formula of volume of cube = $(side)^{3}$

and formula of surface area of cube = $6(side)^{2}$

Step 1:

We have ratio of volume of cube = $\frac{8}{27}$

⇒$\frac{x^{3} }{y^{3} } = \frac{8}{27}$ ⇒$\frac{x}{y} = \frac{2}{3}$

Now ,  ratio of surface are of  cube = $\frac{6x^{2} }{6y^{2} }$   ⇒$(\frac{x}{y} )^{2}$

Now put the value of $\frac{x}{y}$  in surface area  of cube we get ,

$(\frac{x}{y} )^{2}$ = $(\frac{2}{3} )^{2}$ = $\frac{4}{9}$ .

Final answer:

Hence , the ration of total surface areas is 4:9 .

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