12.6 Surface Area and Volume of

SpheresUnit V Day 6

Do Now

• List the formulas:• Euler’s theorem• Volume of prism• Volume of cylinder• Surface area of prism• Surface area of cylinder• Volume of pyramid• Volume of cone

Finding the Surface Area of a Sphere

• We know that a circle is the set of all points in a plane that are a given distance from a point.

• A sphere is the set of all points in space that are a given distance (radius) from a given point (center).

Ex. 1: Finding the Surface Area of a Sphere (baseball)

• A baseball and its leather covering are shown. The baseball has a radius of about 1.45 inches.

a. Estimate the amount of leather used to cover the baseball.

Theorem 12.11: Surface Area of a Sphere

• The surface area of a sphere with radius r is S = 4r2.

Ex. 1: Finding the Surface Area of a Sphere

• Find the surface area of each sphere.

• When the radius doubles, does the surface area double?

Finding the Volume of a Sphere

• Let n be the number of pyramids needed to fill the sphere.

• The volume of each pyramid is __________.

• The sum of the base areas is _____. This is the __________________, which is ______.

• You can approximate the volume V of the sphere as _____________.

Theorem 12.12: Volume of a Sphere

• The volume of a sphere with radius r is S = 4/3 r3. 3

Ex. 4: Finding the Volume of a Sphere (ball bearings)

• To make a steel ball bearing, a cylindrical slug is heated and pressed into a spherical shape with the same volume. Find the radius of the ball bearing to the right.

Closure

• How can you find the surface area of a sphere? the volume of a sphere?