Find the volume of a cone if the radius of its base is 1.5 cm and its perpendicular height is 5 cm.

Solution The formula for the volume of a cone is: $$V = \frac{1}{3}\pi r^2 h$$ where: $V$ = volume of the cone $$\pi$$ = pi (approximately 3.14) $$r$$ = radius of the base of the cone $$h$$ = height of the cone, measured along its perpendicular axis Substituting the given values, we get: $$V = \frac{1}{3}\pi (1.5 \text{ cm})^2(5 \text{ cm})$$ $$V = \frac{1}{3}\pi (2.25 \text{ cm}^2)(5 \text{ cm})$$ $$V = \frac{1}{3}\pi (11.25 \text{ cm}^3)$$ $$V = (3.75)\pi \text{ cm}^3$$ $$V \approx 11.78 \text{ cm}^3$$ Therefore, the volume of the cone is approximately 11.78 cubic centimeters.