Question

PLEASE HELP ME!

Jessica has 400 cm^3 of material. She uses 35cm^3 to make a right triangular prism. She wants to make a second prism that is a dilation of the first prism with a scale factor of 2.5
How much more material does Jessica need in order to make the second prism?

Answer 1

181.875 cm³

Explanation:

You want to know the amount of additional material Jessica needs to make a prism with a volume of 35 cm³ and one that is dilated by a factor of 2.5, given that she has 400 cm³ of material.

Larger volume

The dilation factor for volume is the cube of the linear dilation factor:

2.5³ = 15.625

so the volume of the scaled-up prism will be ...

(35 cm³) × 15.625 = 546.875 cm³

Total volume

The total volume of material Jessica needs for the two prisms is ...

35 cm³ + 546.875 cm³ = 581.875 cm³

Needed

Since Jessica has 400 cm³ of material, the amount she needs is ...

581.875 cm³ - 400 cm³ = 181.875 cm³

Jessica needs 181.875 cm³ more material to make the second prism.