Question

A display case for the artifact is in the shape of a cube. Each side of the display case is three times longer than the width of the artifact.

Artifact Lenght and Width: W(in)
The artifact is a square pyramid.

A. Write an expression for the volume of the case. Write your answer as a power.
B. Simplify the expression.

Answer 1

So Ill assume that the artifact is a square pyramid?

Answer 2

Yes

Answer 3

1/3(a^2)(h) where a is a base edge and h is height is the formula for volume of a square pyramid

Answer 4

what do you think will happen if each side of the display case is three times longer than the width of the artifact.

Answer 5

Wait, my question was, is the display case also a square pyramid?

Answer 6

What is a box?

Answer 7

Read the first sentence.

Answer 8

Ah. My bad.
So the volume of a cube is just going to be side length times side length times side length

Answer 9

Times side length.

Answer 10

So the width of the square pyramid is represented by W.
The sides of the display case are represented by 3w. One side = 3w.
So volume is side length cubed right?

Answer 11

So the volume of the square would be (3w)^3

Answer 12

Try part 2 on ur own

Answer 13

Thank you

Answer 14

Get part 2?

Answer 15

Is it 27w^3

Answer 16

You got it :)

Answer 17

Thanks again

Answer 18

Wait, is (3w)^3 written as a power?

Answer 19

wdym?

Answer 20

A. Write an expression for the volume of the case. Write your answer as a power.

Answer 21

Oh yeah, That is what the problem is asking.

Answer 22

\(\color{#0cbb34}{\text{Originally Posted by}}\) @darkknight
Oh yeah, That is what the problem is asking.
\(\color{#0cbb34}{\text{End of Quote}}\)
Yes, but is (3w)^3 written as a power, or is it just an expression?

Answer 23

it is an expression. and also a power.

Answer 24

written as a power and expression i mean

Answer 25

Than part 2 was to simplify.

Answer 26

Okay, thank you.

Answer 27

Np