What does the volume of a sphere mean?
The volume of a sphere represents the space within the ball-like figure.
Volume of a sphere = ⁴⁄₃πr³
What does the surface area of a sphere mean? The surface area of a sphere represents the area of the outside of a sphere.
Surface Area =
(r represents the radius of the sphere)
How can we use the concept:
Π-stands for pi which we are going to use as 3.14.
r-stands for radius which is an imaginary line that goes from the center to an endpoint on the sphere.
d-stands for diameter which is an imaginary line that goes from one endpoint on the circle through the center to the other side of the circle. Diameter is half of the radius.
Volume:
V = ⁴⁄₃πr³ is the formula for the volume of the sphere.
Radius = 3m. V = ⁴⁄₃πr³ Substitute in the numbers and use 3.14 for π
V = ⁴⁄₃ (3.14)(3)³ Simplify your problem by order of operations
V = ⁴⁄₃ (3.14)(27) Now multiply ⁴⁄₃ by the equation and simplify
V = 113.04 m³
Surface Area:
SA = 4πr
2 is the formula for the surface area of the sphere.
Radius = 4m
SA =
Substitute in the numbers and use 3.14 for π
SA =
Simplify your problem by order of operations
SA = (4)(3.14)16 Now multiply 4*3.14*16 by the equation and simplify
SA =
Sample Math Problems
1) V = ⁴⁄₃πr³ Diameter = 12 in
Solution: Because they gave us a diameter in this problem we will now need to take half of the diameter so that we can have the radius. The radius is used in the problem.
Diameter is 12 inches, therefore radius will be 6.
V = ⁴⁄₃πr³
V = ⁴⁄₃(3.14)(6)³
V = ⁴⁄₃ (3.14)(216)
V = 904.32 in³
2. Radius = 10m
Round the following answer to the nearest hundredth.
V = ⁴⁄₃πr³
V = ⁴⁄₃(3.14)(10)³
V = ⁴⁄₃(3.14)(1000)
V = 4,186.67 m³
3. Find the volume of the sphere.
Diameter of a sphere = 15 cm³
Radius of the sphere will be 7.5 cm³.
Round the following answer to the nearest tenth.
Solution:
V = ⁴⁄₃πr³
V = ⁴⁄₃(3.14)(7.5)³
V = ⁴⁄₃(3.14)(421.875)
V = 1766.25 cm³
1. SA =
