9-2D Surface Area and Volume of Spheres How many bases does a sphere have? What measurement do you need to know in a sphere? What is the formula for the surface area of a sphere? What is the formula for the volume of a sphere?

How many bases….. Does a prism have? Does a pyramid have? Does a cylinder have? Does a cone have? Does a sphere have?

Sphere Measuring What one measurement do you need to know when working with a sphere? The center? The diameter? The radius? No ? yes

Theorem The surface area of a sphere is 4π times the square of its radius. SA = 4 π r 2

Find the Surface Area of the Sphere SA = 4π r 2 SA = 4π(5) 2 SA = 100π (exact) SA ≈ (approx) r = 5

Theorem The volume of a sphere is four-thirds the product of π and the cube of its radius. V = 4 / 3 π r 3

Find the Volume of the Sphere V = 4 / 3 π r 3 V = 4 / 3 π (5) 3 V = 166⅔π (exact) V ≈ (approx) r = 5

Find the Volume and the Surface Area of a sphere… When the area of one its great circles is 4π. What do circle area and sphere volume/surface area have in common? Radius!!! A = 4π

Find the Volume and the Surface Area of a sphere… A = πr 2 4π = πr 2 r 2 = 4 r = 2 V = 4 / 3 π r 3 V = 4 / 3 π (2) 3 V= 10⅔π V ≈ 33.5 A = 4π SA = 4πr 2 SA = 4π(2) 2 SA = 16π SA ≈ 50.3

Find the volume of a sphere whose surface area is 36π SA = 4 π r 2 36π = 4π r 2 9 = r 2 r = 3 V = 4/3 π r 3 V = 4/3 π (3) 3 V = 36π V ≈ SA =36π

Tennis Anyone? A cylindrical can of tennis “spheres” contains three balls. The radius of each ball is about 3.25 cm. Find the dimensions of the can. Find the volume of the can. Find the volume of the tennis balls. H = 19.5,r= 3.25 V = V =

How many bases does a sphere have? 0 What measurement do you need to know in a sphere? radius What is the formula for the surface area of a sphere? SA = 4 π r 2 What is the formula for the volume of a sphere? V = 4/3 π r 3

Assignment 9-2D Page 641, 1-6, No Formulas with numbers No Credit