Question

ratio of surface areas of two cubes is 16:25.find the ratio of their volumes.

Answer 1

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Answer 2

Answer:

Ratio of volumes ofthe cubes is 64:125.

Step-by-step explanation:

Let the edges of the cubes be x and y.

Then,

Surface area of cube = 6 ☓ side^2

✔️ Surface area of cube 1 = 6 ☓ x^2.

✔️Surface area of cube 2 = 6 ☓ y^2.

Ratio of surface area :

6x^2/6 y^2 = 16/25

X^2/y^2 = 16/25

(x/y)^2 = (4/5)^2.

Therefore,

x/y = 4/5.

✔️Ratuo of sides = 4 : 5.

➡️ Volume of cube = edge ^3.

Volume of cube 1 = x^3.

Volume of cube 2 = y^3.

✔️Ratio of volumes = x^3/y^3.

➡️ x^3/y^3 = (x/y) ^3

Or

Ratio of volumes = (x/y) ^3

➡️ (x/y) ^3 = (4/5)^3

➡️ (x/y) ^3 = 64/125

➡️ x^3/y^3 = 64/125

Ratio of volumes of cubes= 64 : 125.