Finding the radius of a hemisphere depends on what information you already have about it. The most straightforward method, especially if you know the diameter, is directly related to the diameter of its circular base.
Finding the Radius Using the Diameter
As mentioned in the reference, we can use the formula:
r = ½ d
Where:
- r is the radius of the hemisphere (and its circular base)
- d is the diameter of the circular base of the hemisphere
The radius is always exactly half the length of the diameter across the same circle.
Understanding the Relationship: Diameter and Radius
Think of the circular base of the hemisphere. The diameter is the distance across the circle passing through its center. The radius is the distance from the center to any point on the edge of the circle.
| Measurement | Definition | Formula Relationship with Radius (r) |
|---|---|---|
| Radius (r) | Distance from center to edge | r |
| Diameter (d) | Distance across circle (through center) | d = 2r |
Therefore, if you know the diameter, simply divide it by 2 to find the radius.
Example
Suppose the circular base of a hemisphere has a diameter (d) of 10 centimeters.
Using the formula:
r = ½ d
r = ½ * 10 cm
r = 5 cm
The radius of the hemisphere is 5 centimeters.
Other Ways to Find the Radius
While the diameter method is simple, you can also find the radius if you know other properties of the hemisphere, such as its volume or surface area, by using the respective formulas and solving for 'r'. However, the most direct approach when the diameter is known is the formula r = ½ d.
