To find the surface area think of a baseball, remove its covering, and find its area. For the volume, use the fact that three hemispheres of a sphere with radius r fill up a cylinder with radius r and height 2r.
Our job is to find the surface area and the volume of the sphere.
Surface Area
To find the surface area, let's consider a baseball and remove the covering.
As we can see, each cover is made of two circles with radius r. Since there are two equal covers, we have that the area of the entire covering is the sum of the area of the four circles.
S = π r^2 + π r^2 + π r^2 + π r^2
⇓
S = 4Ď€ r^2
Volume
To find the volume of the sphere, we will consider a cylinder with radius r and height 2r. Notice this cylinder is circumscribed about the sphere.
If we want to fill the cylinder with sand by using half of the sphere (a hemisphere), it will take three hemispheres to fill the cylinder.
From the above we have that the volume of the cylinder is three times the volume of a hemisphere of the sphere.
V_(cylinder) = 3* V_(hemisphere)
Now, since a hemisphere is half of the sphere, its volume is half the volume of the sphere. Let's substitute it into the formula above and solve it for the volume of the sphere.
