# What is the difference in volume between a baseball with a diameter of 1.75 in and a soccer ball with a diameter of 9.50 ​in?

May 6, 2018

The difference in volume is approximately ${\text{446 in}}^{3}$ or ${\text{0.26 ft}}^{3}$.

#### Explanation:

You need to start with the formula of the volume for each. In addition, we will think of the balls as totally spherical. This is, of course, an approximation.

If a sphere has a radius of r, then the volume

$V = \frac{4}{3} \pi {r}^{3}$, where the diameter $= 2 r$

The radius of the baseball is

$r \setminus \text{in" =1.75/2 \ "in" = 7/8 \ "in}$

The radius of the soccer ball is

$R \setminus \text{in" =9.5/2 \ "in" = 38/8 \ "in}$

(to ensure we use the same unit for both).

This gives the two volumes as:

• baseball: $V = \frac{4}{3} \pi {r}^{3} = \frac{4}{3} \pi {7}^{3} / {8}^{3} = {7}^{3} / \left(3 \cdot {2}^{7}\right) \pi$
• soccer ball: $V = \frac{4}{3} \pi {R}^{3} = \frac{4}{3} \pi {38}^{3} / {8}^{3} = {38}^{3} / \left(3 \cdot {2}^{7}\right) \pi$

The difference in volume, then, is

$\frac{{38}^{3} - {7}^{3}}{3 \cdot {2}^{7}} \pi \setminus {\text{in"^3~~446 \ "in}}^{3}$

As

${\text{1 ft"^3 = "1728 in}}^{3}$

this gives a difference roughly equal to ${\text{0.26 ft}}^{3}$.

May 6, 2018

Difference in volume$= {\text{446.114 inches}}^{3}$

#### Explanation:

Volume of a sphere$= \frac{4}{3} \pi {r}^{3}$

Diameter of baseball$= 1.75$inches

radius$= \frac{1.75}{2} = 0.875$inches

$\therefore V = \frac{4}{3} \cdot \pi \cdot {0.875}^{3}$

$\therefore V = \frac{4}{3} \cdot 3.141592654 \cdot 0.669921875 = {\text{2.806 inches}}^{3}$

~~~~~~~~~~~~~~~~

Volume of a sphere$= \frac{4}{3} \pi {r}^{3}$

Diameter of soccer ball$= 9.5$inches

radius$= \frac{9.5}{2} = 4.75$inches

$\therefore V = \frac{4}{3} \cdot \pi \cdot {4.75}^{3}$

$\therefore V = \frac{4}{3} \cdot 3.141592654 \cdot 107.171875 = {\text{448.920 inches}}^{3}$

Difference in volume$= 448.920 - 2.806 = {\text{446.114 inches}}^{3}$