Question

Jake has 900 cm³ of material. He uses 14.5 cm³ to make a right triangular prism. He wants to make a second prism that is a dilation of the first prism with a scale factor of 4.
How much more material does Jake need in order to make the second prism?

Select from the drop-down menu to correctly complete the statement.

Jake needs an additional (13.5, 28, 42.5)
cm³ of material to make the second prism.

1. Jake needs an additional 42.5 cm³ of material to make the second prism.

### Amount of material available

Since Jake has 900 cm³ of material and he uses 14.5 cm³ to make a right triangular prism. The amount of material available to make the second prism is V = 900 cm³ – 14.5 cm³
= 885.5 cm³

### Scale factor

Now, the second prism is gotten by ditaion of the first prism by a factor of 4.
Since we have volume, (scale  factor)³ = volume of second prism/volue of first prism

### Volume of second prism

So, volume of second prism, V’ = (scale factor)³ × volume of first prism = 4³ × 14.5 cm³ = 928 cm³

### Amount of material more needed

So, the amount of material more needed to make the second prism is V”‘ = V’ – V = 928 cm³ – 885.5 cm³
= 42.5 cm³
So, Jake needs an additional 42.5 cm³ of material to make the second prism.