Table of Contents 43. Surface Area & Volume of Spheres

Surface Area & Volume of Spheres Std – MM2G3 Understand properties of circles Essential Question – What is the difference between surface area and volume?

Definition Sphere – A round solid figure, with every point on its surface equidistant from its center.Sphere – A round solid figure, with every point on its surface equidistant from its center.

Surface Area of a Sphere S = 4  r 2 (it takes 4 circles to cover a sphere)

Example Ex: Find the surface area of a sphere with a radius of 8 cm. S = 4  (8) 2 S = 4  (64) S = 256  cm 2

Example Find the radius of a sphere with surface area of 200 cm 2 SA = 4  (r) = 4  (r) = (r) 2 r = 3.99 cm

More Definitions Hemisphere – ½ of a sphere.Hemisphere – ½ of a sphere. Great Circle of a Sphere – the cross section of a sphere sliced by a plane through its center.Great Circle of a Sphere – the cross section of a sphere sliced by a plane through its center. ** Every great circle splits a sphere into 2 hemispheres.

Ex: The circumference of a great circle of a sphere is 15.5  m. What is the surface area of the sphere? C = 2  r 15.5  = 2  r 15.5 = 2r 7.75 m = r S = 4  r 2 S = 4  (7.75) 2 S = 4  ( ) S =  m 2 Or m 2

Volume of a Sphere

Example Find the volume of a sphere with a radius of 3 ft. V = 36  ft 3 or ft 3

Example Find the radius of a sphere with a volume of 2304  cm 3

Example If it takes 36π in 3 of air to fill a basketball, find its surfaced area