Question

The areas of three of the faces of a right, rectangular prism are $24 \hspace{.6mm} \mathrm{cm}^2$, $32 \hspace{.6mm} \mathrm{cm}^2$, and $48 \hspace{.6mm} \mathrm{cm}^2$. what is the volume of the prism, in cubic centimeters?

Answer 1

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:

$(L*H)(L*W)(W*H) = 24*32*48 \\ \\ L^2 W^2 H^2 = 36864$

By taking square root on both sides,

$L*W*H= 192$

So, the volume of the rectangular prism will be 192 cubic centimeter or cm³ .