Question

1) What is the maximum volume of a pyramid that can fit inside a cube with a side length of 12 cm?

Answer 1

Answer:

1) 576

2) 6720

Step-by-step explanation:

1) A cube with side lengths of 12cm means that the pyramid's base length, base width, and height are all limited to 12cm. Plugging this into the formula for the volume of a pyramid, you get l*w*h/3=576 cubic centimeters. (btw i'm a bit shaky on this one because I haven't really though about the different possible arrangements of the pyramid inside the square)

2) Because you know the slant height and the base, you can use the Pythagorean theorem to find the height of the pyramid. Half of 24 is 12, so $\sqrt{37^2-12^2}=35$. Using the formula for the volume of a pyramid, you get 24*24*35/3=6720. Hope this helps!