Answer:
Volume of the empty space (outside pyramid) is 225 cm².
Step-by-step explanation:
Dimensions of the rectangular prism = 5cm × 5cm × 12cm
Volume of a triangle is represented by the expression,
[tex]V_{1}[/tex] = Length × Width × Height
= 5×5×12
= 300 cm²
A rectangular pyramid with half the height and same base of the prism, has been inserted inside the rectangular prism then,
Volume of pyramid is represented by the expression,
[tex]V_{2}=\frac{1}{3}(\text{Area of the base})\times (\text{Height})[/tex]
= [tex]\frac{1}{3}(5\times 5)\times (6)[/tex]
= 75 cm²
Therefor, volume of the space left in the blank prism
[tex]V_{1}-V_{2}=300-75[/tex]
= 225 cm²
