12.6 surface area and volume of spheres unit v day 6
TRANSCRIPT
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?