Question

Each dimension of a cube has been increased to twice its original size. If the new cube has a volume of 64,000 cubic centimeters, what is the area of one face of the original cube?

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Answer 1

$\huge\bold{Question}$

Each dimension of a cube has been increased to twice its original size. If the new cube has a volume of 64,000 cubic centimeters, what is the area of one face of the original cube?

$\huge\bold{solution}$

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 2a

The volume of a cube is given by the formula

Volume of a cube a³

Volume of new cube = (2a)³

• 8a = 64000
• a = 8000
• a = ³√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 x 20

Area of one face 400 cm²

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

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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 2a

The volume of a cube is given by the formula

Volume of a cube a³

Volume of new cube = (2a)³

8a = 64000

a = 8000

a = ³√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 x 20

Area of one face 400 cm²

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

Hope it helps ☺️☺️☺️

please don't report answer

if you mark at brain list i will give you 15 thanks ☺️☺️

Step-by-step explanation:

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