Question

if a sphere has a diameter of 10 inches, its radius is inches. the volume of a sphere helps determine the amount of inside it. the volume of a sphere is calculated using the radius raised to the power. in real - world applications, understanding the volume of spheres can help in designing and other objects.

Explanation:

Step1: Find the radius of the sphere

The radius \(r\) of a sphere is half of its diameter \(d\). Given \(d = 10\) inches, so \(r=\frac{d}{2}\).
Substituting \(d = 10\) into the formula: \(r=\frac{10}{2}=5\) inches.

Step2: Recall the concept of volume

The volume of a three - dimensional object measures the amount of space it occupies. For a sphere, the volume formula is \(V=\frac{4}{3}\pi r^{3}\).

Step3: Analyze the power of the radius in the volume formula

In the formula \(V = \frac{4}{3}\pi r^{3}\), the radius \(r\) is raised to the third power.

Step4: Consider real - world applications

In real - world scenarios, understanding the volume of spheres is useful in designing spherical objects. For example, in engineering (a sub - field of Natural Science related to Mathematics in this context), when creating spherical containers (like ball - shaped tanks) or spherical components in machinery.

Answer:

1. \(5\)
2. space
3. third
4. spherical