10.6 Surface Area & Volume of Spheres

Warm up 1. List three spheres you would see in real life. 2. Find the area of a circle with a 6 cm radius. 3. Find the volume of a cylinder with the circle from #2 as the base and a height of 5 cm. 4. Find the volume of a cone with the circle from #2 as the base and a height of 5 cm.

Spheres Sphere – The set of all points in space equidistant from a given point. Radius – Is a segment that has one endpt @ the center & the other endpt on the sphere. r Center Diameter – A segment passing through the center w/ both endpts on the sphere.

Great Circles Great Circle – A cross-section of a sphere that also contains the center of the sphere. Circumference of the Great Circle = Circumference of the sphere. A Great Circle divides the sphere into 2 hemispheres. Any cross section (Great Circle) of the sphere is a circle.

Surface Area of a sphere SA = 4r2 r Radius of a sphere

Ex.1: SA of a sphere Find the surface area of a sphere w/ a diameter of 8m. SA = 4r2 = 4(4)2 = 4(16) = 64 = 201.1m2 4m

Ex.2: Circumference and SA The circumference of the Earth is 24,902miles. Find the Surface Area of the Earth. SA = 4r2 = 4(3963)2 = 197,387,018 miles2 C = 2r 24,902 = 2r r = 3963 miles

Example 3: Find the surface area of the figure below. SA sphere = 4πr² Hemisphere is half but you also have a base. SA = ½(4π6²)+ B =72π + B B = πr² = π6² = 36π SA = 72π + 36π = 108π cm² ≈ 339.3 cm²

Volume of a sphere Vs = (4/3)r3 r Radius of a sphere

Ex.4: Find the volume of the following sphere. Vs = (4/3)r3 = (4/3)(15)3 = (4/3)(3375) = 4500 = 14137m3 30m

Ex.5: SA & Volume The surface area of a sphere is 125in2. Find its volume to the nearest whole number. Vs = (4/3)r3 = (4/3)(3.2)3 = (4/3)(31.4) = 43.7 = 137in3 SA = 4r2 125 = 4r2 r = 3.2in

What have we learned?? Vs = (4/3)r3 r Radius of a sphere SA = 4r2