A sphere is a set of points equidistant from a fixed point O (center of the sphere) at a constant distance R (radius). The formula for calculating the surface area of a sphere is also a straightforward and easy-to-remember concept. In this article below, let's explore the detailed calculation formula of this geometric shape.
How is the surface area of a sphere calculated?
Calculating the surface area of a sphere
- General formula for calculating the surface area of a sphere:
Ssphere = 4 π.R2 (1)
or:
Ssphere = π. d2 (2)
- Explanation of symbols for the variables:
Ssphere : Symbol for the surface area of the sphere
R is the radius of the sphere
d is the diameter of the sphere
π : Pi (π = 3.14)
- Unit of area: square meter (m2
Proving the formula for calculating the surface area of a sphere
The formula for the surface area of a sphere is proven as follows:
Illustrative example of calculating the formula for the surface area of a sphere :
Exercise 1. Calculate the surface area of a sphere with a radius extending from the center O as follows:
a) 8 m
b) 1.3 dm
c) 2 cm
d) 15 cm
Solution
Applying formula (1)
a) The surface area of the sphere is:
4x 3.14 x 82 = 6430.72 (m2)
b) Surface area of the sphere is:
4 x 3.14 x 1.32 = 27.59432 (dm2)
c) Surface area of the sphere is:
4 x 3.14 x 22 = 100.48 (cm2)
d) Surface area of the sphere is:
4 x 3.14 x 152 = 42390 (cm2)
Exercise 2. Calculate the surface area of the sphere given the diameter's length:
a) 2.1 cm
b) 9 cm
c) 1⁄2 cm
d) 4.5 cm
Solution:
Applying formula (2)
a) The surface area of the sphere is:
3.14 x 2.12 = 13.8474 (cm2)
b) Surface area of the sphere is:
3.14 x 92 = 254.34 (cm2)
c) Surface area of the sphere is:
3.14 x (1/2)2 = 0.785 (cm2)
d) Surface area of the sphere is:
3.14 x (4.5)2 = 63.585 (cm2)
* Hint
For these exercises, simply substitute the values into the formula for calculating the surface area of a sphere (1) or (2) and perform the calculations (you can do mental math for simple numbers or use a handheld calculator for complex ones).
How is a spherical surface different from a spherical shape?
- A spherical surface is the outer shell of a sphere; in other words, it is the hollow sphere
+ The spherical surface exists in 3D
+ Its characteristic is surface area
- A spherical shape encompasses both the spherical surface, including the outer part, and the inner part limited by that surface.
+ The spherical shape is in 2D and is a solid sphere
+ Its characteristic is volume.
Before tackling exercises related to calculating the surface area of a sphere, it's crucial to differentiate between the concepts of a spherical surface and a spherical shape. Additionally, the most important step in solving problems is to be familiar with the formulas. Reviewing how to calculate the area of a circle is essential preparation for solving problems related to circles. We hope that our comprehensive article here will help you in your learning and problem-solving journey. We wish you continued enjoyment in studying mathematics in general and geometry in particular.
In addition to understanding the formulas for calculating the surface area of a sphere, it's essential to master the formula for finding the volume of a sphere in the series of exercises related to spheres and spherical surfaces. These are fundamental and crucial concepts that you need to study thoroughly.