12.7 Surface Area of Spheres. Angela Isac Abby Kern 1st hour. Objectives. Recognize and define basic properties of spheres. Find surface areas of spheres. . What is a Sphere?. A sphere is the locus of all points that are a given distance from a given point called the center .
In the figure, O is the center of the sphere, and plane R intersects the sphere in circle A. If AO = 3cm and OB=10cm, find AB.
Use the Pythagorean Theorem to solve for AB.
OB2 = AB2 + AO2Pythagorean Theorem
102 = AB2 + 32OB = 10, AO = 3
100 = AB2 + 9 Simplify.
91 = AB2 Subtract 9 from each side.
9.5 = AB Use a calculator.
Answer: AB is approximately 9.5cm.
If a sphere has a surface area of T square units and a radius of r units, then
T= 4 r2
This is simply saying that the surface area (T) of the sphere is 4 times the area of the great circle ( r2).
Find the surface area of the sphere given the area of the great circle.
Use the formula for surface area to solve.
T = 4 r2Surface are of the sphere.
T = 4(201.1) r2 = 201.1
T = 804.4 Multiply.
Answer: 804.4 in2
Since a hemisphere is half a sphere, to find its surface area, find half of the surface area of the sphere and add the area of the great circle.
T = ½(4 r2) + r2
Find the area of the hemisphere.
Use the formula for the surface area of a
hemisphere to solve.
T = ½(4 r2) + r2 Surface are of a hemisphere
T = ½[4 (4.2)2] + (4.2)2 Substitution
T = 166.3 Use a calculator.
Pre-AP Geometry: Page 674 #10 - 29