Question

A prism is dilated by a factor of 1. 5. How many times larger is the volume of the resulting prism than the volume of the original prism? Enter your answer as a decimal in the box.

Answer 1

The volume of the resulting prism is 3.375 times of original volume.

What is a dilation or scale factor?

The factor by which the dimensions of an object are enlarged is called the scale factor.

Let us take the base area of Prizm = a²

Height of the prism = h

Enlarged area = (scale factor)² * previous area

Enlarged area = 1.5²*a² = 2.25a²

Enlarged height = 1.5h

So, enlarged volume = enlarged area* enlarged height

Enlarged volume= 2.25a²*1.5h = 3.375a²h

Enlarged area/previous area = 3.375a²/a² = 3.375

Therefore, the volume of the resulting prism is 3.375 times of original volume.

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