Quite obviously, one of the most important things in a game is the ball. The larger it is, the harder it is to handle. One way, already discussed, to find the size of a ball is volume. Another is surface area. Surface area (SA) is the area of the boundary of a 3-dimensional figure. A cube with each side 1 has a SA of 6 units2.
Because a cube has 6 equal square surfaces: left, right, front, back, top, and bottom. Then, if each side has a length of 1 unit, the area of each surface is 1 unit2 (1*1=1). Then, adding up the areas of the 6 surfaces, we arrive at the surface area of 6.
The basketball is a sphere, how can I find the SA of a sphere?
Consider a solid sphere is made up of "almost pyramids" with vertices at the center of the sphere. The solid is not exactly a pyramid because its base is not exactly a polygon. Even so, when the base of the "almost pyramid" is small, its volume is close to that of a pyramid, namely 1/3Bh. Since h = r, the radius of the sphere, each "almost pyramid" has volume 1/3Br.
Now break up the entire sphere into "almost pyramids" with bases having areas B1, B2, B3, B4, and so on.
The volume V of the sphere is the sum of the volumes of all the "almost pyramids" with bases B1, B2, B3,........
V = 1/3B1r + 1/3B2r + 1/3B3r + 1/3B4r + ........
V = 1/3r( B1 +B2 + B3 + B4 + ......)
The sum of the bases is the surface area (S.A.) of the sphere. The volume V is 4/3¶3. Substituting,
4/3¶r3 = 1/3r * S.A.
To solve for the surface area, multiply both sides by 3/r.
3/r * 4/3¶r3 = 3/r * 1/3r * S.A.
4¶r2 = S.A.
Sphere Surface Area Formula:
The surface area SA of a sphere with radius r is 4¶r2.
S.A. = 4¶r2
Stumped? Take a look at the answer key![an error occurred while processing this directive]