# S.A. of Sphere

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.

Why?
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

## Great, let me try some problems myself!

1. Find the surface area of a basketball with radius 50 cm. ¶ cm2

2. Find the surface area of a sphere with diameter 100" to the nearest square unit. in2

3. How do the surfaces of the moon and the earth if the moon has diameter about 1/4 that of the Earth? The Moon's surface area is of the earth's surface area.

4. A sphere has volume 36¶ cubic meters. What is the surface area? square meters

5. Find the exact surface area of a sphere with radius 6.

6. A sphere has a surface area of 100¶. What is its diameter?units

7. Jupiter's diameter is 11 times the diameter of Earth. How do their surface areas compare?
Jupiter's SA is times larger than that if Earth.

Stumped? Take a look at the answer key!

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