Let's find the volume of Denise's paperweight step by step.
### Given Data:
1. The base of the pyramid is a square with each side length measuring [tex]\(6 \, \text{cm}\)[/tex].
2. The height of the pyramid (perpendicular distance from the base to the apex) is [tex]\(6 \, \text{cm}\)[/tex].
### Step-by-Step Solution:
1. Calculate the Area of the Base:
The base of the pyramid is a square. The area of a square is given by:
[tex]\[
\text{Area of the base} = \text{side length}^2
\][/tex]
Given that the side length of the square base is [tex]\(6 \, \text{cm}\)[/tex], we can calculate the area:
[tex]\[
\text{Area of the base} = 6 \, \text{cm} \times 6 \, \text{cm} = 36 \, \text{cm}^2
\][/tex]
2. Calculate the Volume of the Pyramid:
The volume [tex]\(V\)[/tex] of a pyramid is given by the formula:
[tex]\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\][/tex]
We already calculated the base area as [tex]\(36 \, \text{cm}^2\)[/tex] and we know the height of the pyramid is [tex]\(6 \, \text{cm}\)[/tex]:
[tex]\[
V = \frac{1}{3} \times 36 \, \text{cm}^2 \times 6 \, \text{cm}
\][/tex]
3. Perform the Calculation:
Multiply the base area by the height:
[tex]\[
36 \, \text{cm}^2 \times 6 \, \text{cm} = 216 \, \text{cm}^3
\][/tex]
Then multiply by [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[
V = \frac{1}{3} \times 216 \, \text{cm}^3 = 72 \, \text{cm}^3
\][/tex]
### Final Answer:
The volume of Denise's paperweight is [tex]\(72 \, \text{cm}^3\)[/tex].
