Chapter 12.6, Problem 9CYU

To determine

To find the surface area of a basketball used in professional game.

Answer to Problem 9CYU

277.01 in²

Explanation of Solution

Given: The circumference of the professional basketball is given as $29\frac{1}{2}$ in.

Formula used:

Surface area of a sphere $=4\pi r^2$

And circumference of great circle of a sphere $=2\pi r$ , where r is the radius of the sphere.

Calculation:

Since basketball is spherical in shape,

  $\begin{array}{l}2\pi r=29\frac{1}{2}\\ \Rightarrow 2\pi r=\frac{59}{2}\\ \Rightarrow r=\frac{59}{2\pi \times 2}\\ \Rightarrow r=4.7\end{array}$

Surface area of the basketball,

  $\begin{array}{l}=4\pi r^2\\ =4·\pi ·{\left(4.7\right)}^2\\ =4\times \pi \times 22.04\\ =277.01\end{array}$

Hence, surface area of the basketball is 277.01 in².