Question

Please answer the question below :)

Answer 1

The volume outside the pyramid but inside the prism is 250 cubic centimeters.

Step-by-step explanation:

Step 1:

First, we determine the volumes of the rectangular prism and the pyramid.

The volume of a rectangular prism is calculated by multiplying its length, its width, and its height.

The length and width are both 5 cm while the height is 12 cm.

The volume of the rectangular prism $= (5)(5)(12) = 300$.

The volume of the prism is 300 cubic centimeters.

Step 2:

The volume of a square pyramid is given by $V = a^{2} \frac{h}{3}$, where a is side length and h is the height of the pyramid.

The height of the pyramid is half of the prism, so $h = 6$ cm and $a=5$ cm.

The volume of the pyramid $= 5^{2} (\frac{6}{3} ) = 50.$

The volume of the pyramid is 50 cubic centimeters.

Step 3:

The volume outside the pyramid but inside the prism $=300 - 50 = 250.$

The volume is 250 cubic centimeters.