Calculating Medicine Capsule Sphere Volume

The question asks us to find the amount of medicine needed to fill a spherical capsule, which means we need to calculate the volume of the sphere. We are given the diameter of the sphere and the value of π.

Key Information from the Question

• Shape of the capsule: Sphere
• Diameter of the sphere: 2.8 mm
• Value of π (π): 22/7
• Required precision: Correct to one decimal place

Sphere Volume Formula

The formula for the volume (V) of a sphere with radius (r) is given by:

\(V = \frac{4}{3} \pi r^3\)

Step-by-Step Volume Calculation

First, we need to find the radius of the sphere from the given diameter. The radius is half of the diameter.

\(\text{Radius} (r) = \frac{\text{Diameter}}{2}\)

\(r = \frac{2.8 \text{ mm}}{2} = 1.4 \text{ mm}\)

Now, we can substitute the values of π and the radius (r) into the volume formula:

\(V = \frac{4}{3} \times \frac{22}{7} \times (1.4 \text{ mm})^3\)

Let's calculate the cube of the radius:

\((1.4)^3 = 1.4 \times 1.4 \times 1.4 = 2.744\)

Now substitute this back into the volume formula:

\(V = \frac{4}{3} \times \frac{22}{7} \times 2.744\)

Combine the fractions:

\(V = \frac{4 \times 22}{3 \times 7} \times 2.744\)

\(V = \frac{88}{21} \times 2.744\)

Now, perform the multiplication and division:

\(V = \frac{88 \times 2.744}{21}\)

\(V = \frac{241.472}{21}\)

Performing the division:

\(V \approx 11.49866\dots\)

The question asks for the answer to be correct to one decimal place. We look at the second decimal place, which is 9. Since 9 is 5 or greater, we round up the first decimal place.

\(V \approx 11.5 \text{ mm}^3\)

Final Calculated Volume

The amount of medicine needed to fill the capsule is approximately 11.5 mm³.

Understanding the Units (mm³)

The volume is measured in cubic millimeters (mm³). This unit represents the three-dimensional space occupied by the medicine inside the spherical capsule. Since the diameter was given in millimeters, the resulting volume is in cubic millimeters.

Revision Table: Sphere Volume Calculation

Additional Information: Related Concepts

Volume is a measure of the amount of space a three-dimensional object occupies. For a sphere, this volume depends only on its radius. A medicine capsule shaped like a sphere provides a uniform dose based on its specific volume.

It's important to use the correct units throughout the calculation. If the diameter was given in centimeters, the volume would be in cubic centimeters (cm³).

The value of π can be approximated in different ways (e.g., 3.14, 3.14159), but using the value provided in the question (22/7) is crucial for getting the expected result in this specific problem.