a regular square pyramid just fits inside a cube (the base of the pyramid is congruent to a face of the cube and the height of the pyramid is equal to the height of the cube). A right cone also just fits inside the same cube the diameter of the base of the cone, the height of the cone, and the height of the cube are all equal.) Which has the larger volume, the cone or the square pyramid?

Question

a regular square pyramid just fits inside a cube (the base of the pyramid is congruent to a face of the cube  and the height of the pyramid is equal to the height of the cube). A right cone also just fits inside the same cube the diameter of the base of the cone, the height of the cone, and the height of the cube are all equal.) Which has the larger volume, the cone or the square pyramid?

anonymous · Answer

@jim_thompson5910

jim_thompson5910 · Answer

let's say we have a cube with side lengths of 1

what is the volume of this cube?

anonymous · Answer

oh wait isn't it 1

jim_thompson5910 · Answer

yes the volume of this cube is 1

jim_thompson5910 · Answer

what is the volume of the pyramid?

anonymous · Answer

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anonymous · Answer

Area of the base * Height * 1/3

jim_thompson5910 · Answer

in this case, L, H and W are all equal to 1

jim_thompson5910 · Answer

you have the correct formula

anonymous · Answer

so which has the larger volume

jim_thompson5910 · Answer

are you able to find the volume of the pyramid that fits inside this 1 by 1 by 1 cube?

anonymous · Answer

yes

jim_thompson5910 · Answer

what is the volume in terms of a number (fraction, decimal or whole number)

anonymous · Answer

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