Jessica has 300 cm³ of material. She uses 12.6 cm³ 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 3. How much more material does Jessica need in order to make the second prism? Select from the drop-down menu to correctly complete the statement. Jessica needs an additional Choose... cm³ of material to make the second prism.

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facundo3141592 facundo3141592 · Answer 1 · 2022-03-31T12:58:22+02:00

Jessica needs another 52.8 cm^3 of material to make the other prism.

For a right triangular prism of base B, height H, and length L, the volume is:

V = (1/2)*B*L*H

Now, we know that the first triangle has a volume of 12.6cm^3, then we can write:

V = 12.6cm^3 = (1/2)*B*L*H

If we dilate the prism with a scale factor of 3, the new dimensions are:

B' = 3B

L' = 3L

H' = 3H

Then the new volume is:

V' = (1/2)*(3B)*(3L)*(3H) = 27*(1/2)*B*L*H

And (1/2)*B*L*H is the original volume, so we can write:

V' = 27*V = 27*(12.6cm^3) = 340.2 cm^3

And she has 300cm^3 and she used 12.6cm^3, so the amount of material that she has left is:

M = 300 cm^3 - 12.6 cm^3 = 287.4 cm^3

Then the amount of material that she needs is:

340.2 cm^3 - 287.4 cm^3 = 52.8 cm^3

So Jessica needs another 52.8 cm^3 of material to make the other prism.

If you want to learn more about volumes, you can read:

https://brainly.com/question/1972490