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# So question help

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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

Jul 5, 2020

#1
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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 Jul 5, 2020
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wow thx a lot! I guess i had it in my mind that it had to be a 30-60-90 triangle... THANK YOU SO MUCH!!!

Guest Jul 5, 2020
#3
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You are welcome ! ElectricPavlov  Jul 5, 2020