The surface area of a sphere is the number of units (cm) that cover the outer surface of a spherical object. The formula that Aristotle, a philosopher and mathematician from Greece discovered thousands of years ago, to find the surface of this sphere, is quite simple even though it is not at all original. The formula is (4πr2), r = radius (or radius) of the circle.
Step
Step 1. Know the variables of the formula
Surface area of the sphere = 4πr2. This ancient formula is still the easiest way to find the surface area of a sphere. You can enter the radius number into any type of calculator to find the surface area of a sphere.
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r, or "radius":
Radius is the distance from the center of the sphere to the edge of the surface of the sphere.
- , or "pi":" This number (which is often rounded to 3.14) represents the ratio between the circumference and the diameter of a circle, and is useful in all equations involving circles and spheres. Pi has an infinite number of decimal places, but is generally rounded to 3.14.
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4:
Due to complex reasons, the surface area of a sphere is always equal to 4 times the area of a circle with the same radius.
Step 2. Find the radius of the sphere
Sometimes, problems have given a radius number to find the area of a circle. However, you often have to find it yourself. For example, a sphere with a diameter of 10 cm has a radius of 5 cm.
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Advanced Tips:
If you only know the volume of a sphere, the radius can be found with a little effort. Divide the volume by 4π, then multiply the result by 3. Finally, take the cube root of the result to get the radius of the sphere.
Step 3. Square the radius
You can do this manually by calculating the multiplication (52 = 5 * 5 = 25) or using the “square” function on the calculator (sometimes labeled as “x2").
Step 4. Multiply the result by 4
While you can multiply the radius by 4 or pi first, it's usually easier if you put 4 first, because it doesn't involve decimals.
If the radius of the sphere is 5, the calculation is 4 * 25 *, or 100π
Step 5. Multiply the result by pi (π)
If the problem asks for an "exact value" of the area of a sphere, write down the product of the radius squared by 4 and end with the symbol. Otherwise, use =3, 14 or the key on the calculator.
- 100 * = 100 * 3, 14
- 100π = 314
Step 6. Don't forget to include units (or units) in your final answer
Is the surface area of the sphere 314 cm, or 314 m? Units must be written as "unit2, " because it expresses area, which is also known as “unit squared”
- The full answer for the sphere in the figure is: Surface Area = 314 units2.
- Units used always is the same as the unit for measuring radius. If the unit of measurement for radius is meters, your answer must also be in meters.
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Advanced Tips:
Units are squared because area reflects the number of flat squares that fit to fill the surface of a sphere. Say, we measure the practice problem in cm. That is, on the surface of a sphere with a radius of 5 cm, we can enter 314 squares, each side of which is 1 cm long.
Step 7. Do the practice questions
If the radius of the sphere is 7 cm, what is the outer surface of the sphere?
- 4πr2
- r = 7
- 4*π*72
- 49 * 4 *
- 196π
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Answer:
Surface Area = 615.75 centimeters2, or 615.75 centimeters squared.
Step 8. Understand the surface area
The surface area of a sphere is the area that covers the outer surface of the sphere. Think of it as a layer of rubber that wraps around a soccer ball, or the surface of the earth. Because the surface of a sphere is curved, its surface area is more difficult to measure than a sphere. As a result, a formula is needed to find the surface area.
- A circle that is rotated on its axis will produce a ball. Think of it like a coin that is rolled on a table and looks like a ball. Although not explained in detail here, that is the origin of the formula for finding the surface area of a sphere.
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Advanced Tips:
Spheres tend to have a smaller surface area per volume than other shapes. That is, the area where the ball can accommodate various objects is smaller than other forms of space.
