Question

If the volumes of two cubes are in the ratio of 64:125, then what is the ratio of their total surface areas?

Give explanation.​

Answer 1

Given :-

Ratio between the volumes if the cubes is 64 : 125

Let their volumes be 64 cubic units and 125 cubic units respectively.

And the sides the cubes be x and y respectively.

We know that,

Side³ = volume of a cube

➡ x³ = 64 cubic units

➡ x = ³√64

➡ x = 4 units

Similarly,

➡ y³ = 125 cubic units

➡ y = ³√125

➡ y = 5 units

The ratio between their surface area = (6x)²/(6y)² [since surface area of a cube = 6(side²)]

= 6(4)²/6(5)²

= (6 × 16)/(6 × 25)

= 96/150

= 16/25

Hence, ratio of their total surface areas is 16 : 25

Answer 2

Answer:

hi mates this is ur answer

Step-by-step explanation:

Let their volumes be 64 cubic units and 125 cubic units respectively.

The sides of the cubes be x and y respectively.

Side³ = volume of a cube

x³ = 64 cubic units

x = ³√64

✍✍x = 4 units✍✍✍

Similarly,

y³ = 125 cubic units

y = ³√125

✍✍ y = 5 units✍✍

The ratio between their surface area = (6x)²/(6y)² [since surface area of a cube = 6(side²)]

The ratio between their surface area = (6x)²/(6y)² [since surface area of a cube = 6(side²)]= 6(4)²/6(5)²

The ratio between their surface area = (6x)²/(6y)² [since surface area of a cube = 6(side²)]= 6(4)²/6(5)²= (6 × 16)/(6 × 25)

The ratio between their surface area = (6x)²/(6y)² [since surface area of a cube = 6(side²)]= 6(4)²/6(5)²= (6 × 16)/(6 × 25)= 96/150

= 16/25

So the ratio of the total surface areas is 16:25...

hope this helps u..