Given:
• Side length of base = 18.2 centimeters
,
• Height of pyramid = 23.1 centimeters
,
• Mass of pyramid = 2.75 kilograms
Let's find the volume of the pyramid.
To find the volume of the pyramid, apply the formula:
[tex]V=a^2\times\frac{h}{3}[/tex]
Where:
a is the side length of the base = 18.2 cm
h is the height = 23.1 cm
Input values into the formula and solve for the volume, V.
[tex]\begin{gathered} V=18.2^2\times\frac{23.1}{3} \\ \\ V=331.24\times7.7 \\ \\ V=2550.55cm^3 \end{gathered}[/tex]
Therefore, the small solid pyramid has a volume of approximately 2550.55 cubic centimeters.
• Part 2.
Find the mass of the pyramid in grams.
Given the mass = 2.75 kilograms
To find the mass in grams, apply the standard unit of measurement.
Where:
1 kilogram = 1000 grams
Thus, we have:
[tex]2.75kg=2.75\times1000=2750\text{ grams}[/tex]
Therefore, the mass in grams is 2750 grams.
• Part 3.
Let's find the density of the pyramid in grams per cubic centimeter.
To find the density, apply the formula:
[tex]density=\frac{mass}{\text{volume}}[/tex]
Thus, we have:
[tex]\begin{gathered} density=\frac{2750\text{ }}{2550.55} \\ \\ \text{density}=1.08\text{ g/}cm^3 \end{gathered}[/tex]
Therefore, the density is 1.08 grams per cubic centimeter.
ANSWER:
Part 1: 2550.55 cubic centimeters
Part 2: 2750 grams
Part 3: 1.08 grams per cubic centimeter.
