Chapter 10.1, Problem 25E

To determine

To calculate:

The probability that a point chosen at random inside the cube is also inside a sphere.

Answer to Problem 25E

The probability that a point chosen at random inside the cube is also inside a sphere is $0.524$ .

Explanation of Solution

Given information:

  

Calculation:

The question is related to probability of the event.

It is given that information about the radius of the provided cube, and sphere inscribed in it and it is used to obtain a probability of randomly selected point being in the cube and sphere.

Thus probabilities that a randomly selected point in the cube, is also in the spheres is obtained as below,

  $P$ (Point in sphere also)

  $\begin{array}{l}=\frac{\frac{4}{3}\pi {\left(\frac{r}{2}\right)}^3}{r^3}\\ =0.524\end{array}$

Hence, The probability that a point chosen at random inside the cube is also inside a sphere is $0.524$ .