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the surface area of a rectangular prism is increased by a factor of 16. by what factor is the volume of the figure increased?

volume of the rectangular prism will increase by a factor of 64.

Step-by-step explanation:

The surface area of a rectangular prism is increase by a factor of 16.

We know surface area is calculated by multiplication of 2 dimensions.

A ∝ length²

√A ∝ length

Therefore, increase in length of the sides will be = √16 = 4

Now we know volume is a unit in which 3 dimensions are multiplied ( length × width × height )

If Increase in length of sides is 4 times then volume will increase by 4³

V ∝ length³

V ∝ (4 × length)³ = 64 × (length)³

Therefore, volume of the rectangular prism will increase by a factor of 64.

D. 64

Step-by-step explanation:

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