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A cube has a surface area of 96 square inches. If 16 cubes are
combined to make a rectangular prism, what is the volume of the
rectangular prism?

Respuesta :

areye028

Answer:

Step-by-step explanation:

A cube has 6 square faces with equal areas by definition. So a cube with a surface area of 96 units would have the surface area of each side be 96/6 = 16 square units.

Because each face of a cube is a square, it has 4 equal sides. This means that each side of the square is 16/4 = 4 units in length. Since each side of the square face is also an edge of the cube, and the way to calculate the volume of a cube is (length of an edge)^3, this means that the volume of the cube must be 4^3 = 64 cube units.

Volume of Cube = 64 cube units.

The volume of the rectangular prism formed by 16 cubes of each surface area of 96 square inches is 1024 inches³

Volume of a cube

volume of a cube = l³

where

  • l = side length

Therefore,

Surface area of a cube = 6l²

Hence,

96 = 6l²

l² = 96 / 6

l = √16

l  = 4 inches

Therefore,

volume of each cube = 4³ = 64 inches³

16 cubes forms the rectangular prsim. Therefore,

volume of rectangular prism = 16(64) = 1024 inches³

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