Volume of Rectangular Prism in a Sphere

A rectangular prism is inscribed in a sphere with a radius of 10 cm. The lengths of the edges of the rectangular prism are in the ratio 3:4:5. What is the volume of the rectangular prism?

Use the formula for the volume of a rectangular prism, which is given by:

$V = l \times w \times h$

where $l$, $w$, and $h$ are the length, width, and height of the prism respectively.

We also need to consider that the diagonal of the rectangular prism corresponds to the diameter of the sphere, which means:

$d = \sqrt{l^2 + w^2 + h^2}$

Given that the diameter of the sphere is $d = 2 \times 10 = 20$ cm.