## anonymous 5 years ago The ratio of the surface areas of two cubes is 49/81 What is the ratio of their volumes?

1. anonymous

thats fairly easy

2. anonymous

surface area of a cube is 6a^2 , where a is the side length

3. anonymous

so let one cube have side length x, the other have side length y

4. anonymous

so 6x^2 / 6y^2 = 49 / 81

5. anonymous

now we want the ratio of volume volume of a cube is a^3

6. anonymous

therefore the ratio of volumes is (x^3 / y^3 )

7. anonymous

from the first equation we know that x^2 / y^2 = 49/81 so (x/y) = +- 7/9 ( by taking sqrts ) , but we are dealing with lengths ( which must be positive, so take the + case

8. anonymous

so the ratio of volumes = (x^3/y^3) = (x^2 / y^2 ) times (x/y) = 49/81 x 7/9

9. anonymous

= 0.471 as a decimal to 3 decimal places

10. anonymous

i'm alittle confuse

11. anonymous

with what ?

12. dumbcow

$SA \rightarrow \frac{6a ^{2}}{6b ^{2}} = \frac{a ^{2}}{b ^{2}}=\frac{49}{81}$ $\sqrt{\frac{a ^{2}}{b^{2}}} = \sqrt{\frac{49}{81}}$ $\frac{a}{b} = \frac{7}{9}$ $V \rightarrow \frac{a^{3}}{b^{3}} = \frac{7^{3}}{9^{3}}$

13. anonymous

surface area is area, so it is two dimensional, while volume is three dimensional. (square units vs cubed units) you have a ratio of two squares, 49 and 81 being 7^2 and 9^2. therefore the ratio of the lengths of the sides must be 7 to 9 and the ratio of the volumes must be 7^3 to 9^3. dumbcow(nice handle) said it nicely.

14. anonymous

so the ratio is 7:9

15. anonymous

no :|