The volume of the rectangular prism will be 192 cubic centimeter or cm³ .
Lets assume the length of the rectangular prism = L , width = W and height = H
So, the Volume will be: (length)×(width)×(height) = L×W×H
The areas of three of the faces of the rectangular prism are given as 24 cm² , 32 cm² and 48 cm²
Each of the face in a right rectangular prism is in shape of rectangle. So, the formula for area of each face is : (length)×(width)
In the diagram,
Area of the blue shaded face: L×H = 24 cm² ................(1)
Area of the black shaded face: L×W = 32 cm² .................(2)
and Area of the green shaded face: W×H = 48 cm² ...................(3)
Now if we multiply all the equations (1), (2) and (3) together, then we will get:
[tex] (L*H)(L*W)(W*H) = 24*32*48 \\ \\ L^2 W^2 H^2 = 36864 [/tex]
By taking square root on both sides,
[tex] L*W*H= 192 [/tex]
So, the volume of the rectangular prism will be 192 cubic centimeter or cm³ .
