Question

The ratio of the surface areas of two cubes is 49/81 What is
the ratio of their volumes?

Answer 1

thats fairly easy

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

now we want the ratio of volume

volume of a cube is a^3

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

= 0.471 as a decimal to 3 decimal places

Answer 10

i'm alittle confuse

Answer 11

with what ?

Answer 12

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

Answer 13

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.

Answer 14

so the ratio is 7:9

Answer 15

no :|