Answer:
The volume of the right pyramid is 30.17 cm squared.
Step-by-step explanation:
Volume of a Square Pyramid
Volume measures the amount of space that a 3-D object takes up.
Depending on the shape there may or may not be a formula to calculate the shape's volume. In our case, a right pyramid, there is one.
[tex]V=\dfrac{1}{3} s^2h[/tex],
where s is the side length of the pyramid's square base and h is the height of the overall figure (don't confuse this with its slant height).
The slant height is the height of the triangular face of the pyramid.
Solving the Problem
From the given information we can deduce that s = 4 but, the height of the figure remains unknown.
Knowing that,
- the height spans from the apex of the pyramid all the way to the center of the pyramid's base
- the distance from the base's edge to the center is half the length of the base
- the slant height's value is 6 cm
a right triangle can be seen between the slant height, the distance between the pyramid's height and edge and, the pyramid's height itself.
Using Pythagorean Theorem, the height can be found!
[tex]h=\sqrt{6^2-2^2} =\sqrt{36-4} =\sqrt{32} \\\Longrightarrow h = 4\sqrt{2}[/tex]
Now that all the variables in the volume formula is found, all we need to do is plug it in and evaluate!
[tex]V=\dfrac{1}{3} s^2h=\dfrac{1}{3} (4)^2(4\sqrt{2})=\dfrac{1}{3} 64\sqrt{2} \\\\\Longrightarrow V = 30.17cm^2[/tex]
