Question

Each dimension of a cube is increased
to twice its original size. If the new cube
has a volume of 64000 cm°, what is the
area of one face of the original cube?​

Answer 1

Answer:

400

Step-by-step explanation:

Answer 2

Answer:

Area of one face = 400 cm²

Step-by-step explanation:

Given:

• Dimension of the new cube is twice the original one

• Volume of new cube = 64000 cm³

To Find:

• Area of one face of original cube

Concept:

Here we have to first find the side of the original cube and then find the area of the face of the original cube.

Solution:

Let a be the length of side of the original cube

Hence length of side of new cube would be 2 a

The volume of a cube is given by the formula

  Volume of a cube = a³

Volume of new cube = (2a)³

   8a³ = 64000

   a³ = 8000

   a = ∛8000  

   a = 20 cm

Hence the length of side of the original cube = 20 cm

Area of one face of a cube is given by the formula,

  Area of one face = a²

Substituting the datas we get,

  Area of one face = 20 × 20

  Area of one face = 400 cm²

 $\boxed{\bold{Area\:of\:one\:face=400\:cm^{2}}}$

Notes:

→ The total surface area of a cube is given by the equation,  

  TSA of a cube = 6 a²

→ Volume of a cube is given by the formula,

   Volume of a cube = a³