Question

A rectangular prism has a height of 12 centimeters and a square base with sides measuring 5 cm. A pyramid with the same base and half the height of the prism is placed inside the prism as shown in the figure. the volume of the space outside pyramid but inside the prism is blank cubic centimeters

Answer 1

the volume of the prism w/o pyrqmid volume is 200cm^3

pyramid volume is v=(1/3)bh
b=base
h=height

prism volume 5×5×25=300 cm^3

pyramid volune
(1/3)×(5×5)×12=100 cm^3

300-100=200 cm^3

Answer 2

Volume of the empty space (outside pyramid) is 225 cm².

Explanation:

Dimensions of the rectangular prism = 5cm × 5cm × 12cm

Volume of a triangle is represented by the expression,

`V_(1)` = 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,

`V_(2)=(1)/(3)(\text{Area of the base})* (\text{Height})`

=
`(1)/(3)(5* 5)* (6)`

= 75 cm²

Therefor, volume of the space left in the blank prism

`V_(1)-V_(2)=300-75`

= 225 cm²