Final answer:
The diameter of a circle is twice the radius, and the circumference can be found using C = 2πr or C = πd. The circle's area is A = πr², and for a sphere, the volume is 4/3 πr³ and the surface area is 4 πr².
Step-by-step explanation:
The formulas related to a circle that a student inquired about include the circumference, area, radius and diameter of a circle. These are crucial concepts in middle school mathematics.
The diameter of a circle is twice the length of the radius. If 'r' represents the radius, then the diameter 'd' is given by
d = 2r. Accordingly, the radius is half of the diameter: r = d/2.
Circumference
The circumference of a circle, which is the distance around it, is given by C = 2πr or C = πd, where π (pi) is approximately 3.14159.
The area of a circle is the space contained within its perimeter and is calculated using the radius. The formula is A = πr². For example, if you have a circle with a radius of 1.2 meters, using a calculator, you would calculate the area as A = π(1.2 m)² which gives 4.5238934 m². It is important to match the significant figures of the radius, meaning the proper area would be reported as A = 4.5 m², rounded to two significant figures.
Volume and Surface Area of a Sphere
For a sphere, the volume is calculated as 4/3 πr³, and its surface area is 4 πr². This information is useful when comparing circular and spherical shapes.