Welcome to MooMooMath. Today we are going to look at spheres and how to look at both the surface area, and the volume of a sphere. Surface area is very simple, if you look at a circle or a sphere there is a great circle on the inside, and I just highlighted it in red. Now they call it the great circle because it can be drawn inside a sphere. What you are going to do is find the area of that great circle which is just π x r^(2 ). The surface area is kind of like on a beach ball the amount of plastic you would need to create the ball, and it is just four times the great circle. So if you can find the area of the circle you just multiple it by four. So you have 4 x π and in this case the radius is 5 and this becomes 5 squared. So 5 squared is 25, and 25 times 4 is 100 and you just stick the π next to it so it becomes 100 π. Now let’s shift over here and look at volume which is a similar formula. It is four thirds times πr^3 and we will cube that. So all I need for this formula is the radius again. So the radius is five and we will cube it times π times 4⁄3. So 5 cubed is 5 times 5 times 5 which is 125 so 4⁄3 times 125 is 500 over 3 and don’t forget your π and your units are cubed because it is 3 dimensional so take your radius cube it and stick a 1 under it and multiple it by 4⁄3 and you get 500⁄(3 π units cubed) So let’s look at a cheat sheet
Surface Area equals 4 x πr^2
Volume of a Sphere equals 4/3 x πr^3
In this example our radius is 6 and six squared is 36 and 36 times 4 is 144 π units squared.
Now to find the volume use 3 as the radius so 3 cubed is 27 and 27 times 4⁄3 is 36π units cubed so those are the two formulas for volume and surface area of a cube.
The great circle of a sphere a circle drawn on the sphere that includes the center of the sphere. The great circle divides a sphere in half, and contains the diameter. In order to find the area of a great circle you use the formula: π x r^(2 ) . If you know the area of the great circle,you can just multiply it by 4 for the surface area of the sphere.
A sphere has a great circle of 35π units^2. Find the surface area of this sphere.
Surface area equals 4 x35π = 140π units^2
Relationship of the great circle and surface area
Finding the surface area of a sphere using circumference.
Surface Area of a Sphere
What is the Surface Area of a sphere with a radius of 5?
r =radius In the picture it is the distance from A to B
Plug 5 into the formula 4πr^2
The formula for finding the surface area of a sphere equals 4πr^2 r=radius
Step 1. Plug 6 in the formula
Step 2. 4 π6^2 = 4*π* 36
Step 3. Multiply 4*π* 36 = 144π units^2
Step 4 Surface area = 452.16 units^2
What is the surface area of a sphere with a radius of 6?
Step 4. 100 x pi = 314 units^2
Surface Area of a Sphere Formula:
r= radius of the circle
What is a sphere? You can think of a sphere as a circle in three dimensions. A sphere is perfectly symmetrical, does not have any vertices, corners, or edges. In addition, all of the points on a sphere are the same distance from the center. In Geometry, the surface area is the measure of the total area of a three-dimensional object. If you have a rectangular shoe box, it is the area of all six of the faces of the box added together.The surface area of a sphere is the total area of the curved surface. You can also think of the surface area as the amount of wrapping paper needed to wrap a 3D object.