Volume and Population Calculation in a Termite Mound - Real-Life Mathematics

Q. A conical termite mound has a height of 1.4 m and a base of radius 60 cm. If there are three termites per cubic centimetre, how many termites inhabit the mound?

Given:

Height h = 1.4 m = 140 cm

Radius r = 60 cm

To find:

Volume of a cone V = ?

Number of termites = ?

Solution:

Formula for volume of a cone

$$V=\frac{1}{3}\pi r^2 h$$

$$By\; putting\; the\; values\; and\; simplifying$$

$$V=\frac{1}{3}\pi (60)^2(140) = \frac{1}{3}\pi (3600)(140) = 168000\pi \text{ cm}^3$$

Number of termites = density × volume

$$= 3 \times 168000\pi = 504000\pi$$

$$\approx 504000 \times 3.1416 \approx 1.58 \times 10^6$$

Approximately 1,583,000 termites inhabit the mound.