Surface Area and Volume of Pyramids, Cones, and Spheres 10-5, 10-7, & 10-8!! - PowerPoint PPT Presentation

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Surface Area and Volume of Pyramids, Cones, and Spheres 10-5, 10-7, & 10-8!! PowerPoint Presentation
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Surface Area and Volume of Pyramids, Cones, and Spheres 10-5, 10-7, & 10-8!!

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  1. Surface Area and Volume of Pyramids, Cones, and Spheres10-5, 10-7, & 10-8!! I can find the surface areas (lateral and total) of pyramids, cones, and spheres. I can find the volume of pyramids, cones, and spheres. I can solve word problems with surface area and volume of pyramids, cones, and spheres.

  2. Pyramids l

  3. Pyramids The lateral faces of a regular pyramid can be arranged to cover half of a rectangle with a height equal to the slant height of the pyramid. The width of the rectangle is equal to the base perimeter of the pyramid.

  4. Pyramids SA = l + B Lateral Surface Area: LSA = l Total Surface Area: l SA = LSA + B or

  5. Example SA = l + B LSA = l Find the lateral area and surface area of the regular pyramid. Step 1 Find the base perimeter and apothem. P = 6(10) = 60 in. a = Step 3 Find the surface area. Step 2 Find the lateral area.

  6. Pyramids Volume: V = h

  7. Example Find the volumeofthe regular hexagonal pyramid with height equal to the apothem of the base Step 1 Find the area of the base. 2 Step 2 Use the base area and the height to find the volume. = 1296 ft3

  8. Cones

  9. Cones SA = l + Lateral Surface Area: LSA = l Total Surface Area: l SA = LSA + B or

  10. Example Find the lateral area and surface area of the cone. LSA = rℓ = (8)(17) = 136 in2 SA = rℓ+ r2 = 136 + (8)2 = 200 in2

  11. Cones Volume: V = or h V =

  12. Example Find the volume of a cone. Step 1 Use the Pythagorean Theorem to find the height. 162 + h2 = 342 h2 = 900 h = 30 Step 2 Use the radius and height to find the volume. = 2560 cm3

  13. Example Find the volume of a conewith base circumference 25 in. and a height 2 in. more than twice the radius. Step 1 Use the circumference to find the radius. 2r = 25 r = 12.5 Step 2 Use the radius to find the height. h = 2(12.5) + 2 = 27 in. Step 3 Use the radius and height to find the volume. = 1406.25 in3

  14. Spheres

  15. Spheres

  16. Example Find the surface area and volume of the sphere. S = 4r2 S = 4(1)2 S = 4 m2

  17. Example Find the surface area and volume of the hemisphere. S = 2r2 + r2 = 2(11)2 +(11)2 = 363 in2

  18. Example Find the surface area and volume of a sphere with a great circle that has an area of 49 mi2. A = r2 49 = r2 r = 7 S = 4r2 = 4(7)2 = 196 mi2

  19. Example

  20. Example