a rectangular prism has a height of 12 centimetres and a square base with sides measuring 5 centimetres, a pyramid with the same base and half the height of the prism is place inside the prism, the volume of the space outside the pyramid but inside the prism is?

Description:

The base of the prism is a square with sides measuring 5 cm, so its area is

(5cm)*(5cm)= 25 square cm

So the volume of the prism, in cubic cm, is

25*12=300

The volume of a pyramid is (1/3)(area of base)(height) .

It is 1/3 of the volume of a rectangular prism with the same base and height.

So the volume of the pyramid in this problem, in cubic cm, is

1/3*300=100

So the volume of the space outside the pyramid but inside the prism, in cubic cm, is

300-100= 200

=200

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Hope this helps.