10-5: Surface Area of Pyramid and Cone Page 710 17) V = 1107π m3 18) V = 16π/3 in3 19) V = 144π ft3 20) Volume is 1/27 22) V = 240π ft3 24) V = 21π in2 25) V = 25π/6 m3 26) V = 11760π ft3 27) V = 240π cm3 33) C = 10π√3 cm 36) S = 600π yd2 11/19/2018 10:32 PM 10-5: Surface Area of Pyramid and Cone

10-5: Surface Area of Pyramid and Cone 11/19/2018 10:32 PM 10-5: Surface Area of Pyramid and Cone

10-5: Surface Area of Pyramid and Cone Fiesta 11/19/2018 10:32 PM 10-5: Surface Area of Pyramid and Cone

Section 10-6 Geometry PreAP, Revised ©2014 viet.dang@humble.k12.tx.us Spheres Section 10-6 Geometry PreAP, Revised ©2014 viet.dang@humble.k12.tx.us 11/19/2018 10:32 PM 10-5: Surface Area of Pyramid and Cone

10-5: Surface Area of Pyramid and Cone Spheres A sphere is the locus of points in space that are a fixed distance from a given point. A radius of a sphere connects the center of the sphere to any point on the sphere. A hemisphere is half of a sphere. A great circle divides a sphere into two hemispheres 11/19/2018 10:32 PM 10-5: Surface Area of Pyramid and Cone

Volume Formulas for Cylinders Surface Area of a Sphere: SA = 4πr2 Volume of a Sphere: V = (4/3)πr3 where r is the radius 11/19/2018 10:32 PM 10-5: Surface Area of Pyramid and Cone

10-5: Surface Area of Pyramid and Cone Archimedes Tomb Archimedes was the first to discover that the volume of a sphere is 2/3 the volume of the cylinder that circumscribes it. He considered this to be his greatest mathematical achievement. 11/19/2018 10:32 PM 10-5: Surface Area of Pyramid and Cone

10-5: Surface Area of Pyramid and Cone Why… Let’s Derive h = 2r 11/19/2018 10:32 PM 10-5: Surface Area of Pyramid and Cone

10-5: Surface Area of Pyramid and Cone Example 1 Find the volume of the sphere. Give your answer in terms of . 11/19/2018 10:32 PM 10-5: Surface Area of Pyramid and Cone

10-5: Surface Area of Pyramid and Cone Example 2 If the volume of a sphere is 972 m3, what is the radius? 11/19/2018 10:32 PM 10-5: Surface Area of Pyramid and Cone

10-5: Surface Area of Pyramid and Cone Your Turn Find the diameter of a sphere with volume 36,000 cm3. 11/19/2018 10:32 PM 10-5: Surface Area of Pyramid and Cone

10-5: Surface Area of Pyramid and Cone Example 3 Find the volume of the hemisphere. 11/19/2018 10:32 PM 10-5: Surface Area of Pyramid and Cone

10-5: Surface Area of Pyramid and Cone Example 4 Find the volume of the composite figure. 11/19/2018 10:32 PM 10-5: Surface Area of Pyramid and Cone

10-5: Surface Area of Pyramid and Cone Your Turn Find the volume of the composite figure. V = 45 – 18 = 27 ft3 11/19/2018 10:32 PM 10-5: Surface Area of Pyramid and Cone

Investigation Think of a sphere as being constructed by a whole bunch of pyramids. The height of each pyramid would be the radius of the sphere. B n = a whole bunch h = radius of the sphere

Investigation Let’s also say that each of these pyramids is congruent and has a base area of B. Thus, the surface area of the sphere is: B

Investigation Furthermore, the volume of the sphere should be the sum of the volumes of the pyramids. B

Investigation Use the two formulas below to derive a formula for the surface area of a sphere. B 4r2 ≈ nB

10-5: Surface Area of Pyramid and Cone Example 5 Find the surface area of a sphere with diameter 76 cm. Give your answers in terms of . 11/19/2018 10:32 PM 10-5: Surface Area of Pyramid and Cone

10-5: Surface Area of Pyramid and Cone Example 6 Find the volume of a sphere with surface area 324 in2. Give your answers in terms of . 11/19/2018 10:32 PM 10-5: Surface Area of Pyramid and Cone

10-5: Surface Area of Pyramid and Cone Your Turn What is the difference between the volume and surface area of this hemisphere below? 11/19/2018 10:32 PM 10-5: Surface Area of Pyramid and Cone

10-5: Surface Area of Pyramid and Cone Assignment Page 719 13-15 all, 17-22 all, 25, 26 11/19/2018 10:32 PM 10-5: Surface Area of Pyramid and Cone