So I had 2 questions that I am stumped on am i just not smart or are these actually hard.
1. The figure shown is a cube. The distance between vertices B and G is \(5\sqrt{2}\) units. What is the volume of the cube, in cubic units?
I got the answer 500 using the pythagorean theorem and 30-60-90 triangles.
2. The sides of the base of a triangular pyramid are 3, 4 and 5 feet and the altitude is 6 feet. What is the number of cubic feet in the volume of the pyramid?
I got the answer 36 using the base and height.
If you could help that would be great
thx in advance
it is a cube so the sides are the same length....
s^2 + s^2 = diagonal ^2
2 s ^2 = (5 sqrt2)^2
s^2 = 25
s = side length = 5 volume would be 5 x 5 x 5 = 125 units3
1/3 base x height = pyramid volume
base is a 3-4-5 right triangle area = 1/2 * 3 * 4 = 6
1/3 (6) (6) = 12 ft3