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2 years ago

The ratio of the surface area of two cubes is 49:81. Find the ratio of there volumes.

Mathematics

2 answers:

Liono4ka [1.6K]2 years ago

7 0

Answer:

343 : 729

Step-by-step explanation:

A cube is made up of 6 square faces. If each face has a side length of a, we can find the surface area of that cube with the formula $A=6a^2$ , since we'll have 6 faces with area a². Let's call the edge length of the first cube a and the edge length of the second cube b. The ratio between their surface areas is then 6a² : 6b², or simply a² : b². If we compare this to our given ratio 49 : 81, we can see that a² = 49 and b² = 81, or, square rooting both equations, a = 7 and b = 9.

The volume of a cube with a side length a is a³, so the ratio between our cubes here must be a³ : b³. Using the values for a and b we just found, this ratio becomes 7³ : 9³, which we can simplify to 343 : 729.

tia_tia [17]2 years ago

4 0

Answer:

343 : 729

Step-by-step explanation:

If the ratio of the sides of a cube = a : b , then

ratio of areas = a² : b² and

ratio of volumes = a³ : b³

Given ratio of areas = 49 : 81, then

ratio of sides = $\sqrt{49}$ : $\sqrt{81}$ = 7 : 9 , so

ratio of volumes = 7³ : 9³ = 343 : 729

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The ratio of the surface area of two cubes is 49:81. Find the ratio of there volumes.​

The ratio of the surface area of two cubes is 49:81. Find the ratio of there volumes.