A capsule of medicine is in the shape of a sphere of diameter 2.8 mm. How much medicine is needed to fill this capsule (correct to one decimal place)?
$$\pi = \frac{22}{7}$$

Question

A capsule of medicine is in the shape of a sphere of diameter 2.8 mm. How much medicine is needed to fill this capsule (correct to one decimal place)?  
$$\pi = \frac{22}{7}$$

Accepted Answer

The capsule is modeled as a sphere with a diameter of 2.8 mm. The radius of the sphere is calculated as:  
$$
	ext{Radius} = \frac{	ext{Diameter}}{2} = \frac{2.8}{2} = 1.4 \, 	ext{mm}.
$$

The formula for the volume of a sphere is:  
$$
	ext{Volume} = \frac{4}{3} \pi r^3.
$$

Substitute $$\pi = \frac{22}{7}$$ and $$r = 1.4$$:  
$$
	ext{Volume} = \frac{4}{3} 	imes \frac{22}{7} 	imes (1.4)^3.
$$

Calculate step-by-step:  
1. $$ (1.4)^3 = 1.4 	imes 1.4 	imes 1.4 = 2.744 $$.  
2. Multiply: $$ \frac{4}{3} 	imes \frac{22}{7} 	imes 2.744 = 11.5 \, 	ext{mm}^3 $$.

Thus, the volume of the capsule is **11.5 mm³**, which corresponds to option **(a)**.

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