Question

A rectangular solid whose edges are 4 cm, 5 cm, and 7cm is inscribed in a sphere., Find the volume and the surface area of the sphere.

Answer 1

The answer is:
Surface Area=433cm^2
Volume=144.5cm^3

Answer 2

Equation of a sphere with radius r is given by x^2 + y^2 + z^2 = r^2
For a rectangular solid inscribes on a sphere, the sides are 2x by 2y by 2z, putting this into the equation of a sphere, we have
(4/2)^2 + (5/2)^2 + (7/2)^2 = r^2
r^2 = 4 + 25/4 + 49/4 = 45/2
r = sqrt(45/2) = 4.74

Now, volume of sphere is given by 4/3πr^3 = 4/3π(4.74)^3 = 142.3π = 447.1 cm^3
Also, surface area of a sphere is given by = 4πr^2 = 4π(4.74)^2 = 90π = 282.7 cm^2