Geometry Chapter 12 Test Review Key

Geometry C.P. Chapter 12 Test Review Name: Key Name the polyhedron and find the number of faces, vertices, and edges of each. 1. Triangular Prism F = 5 V = 6 E = 9 2. Hexagonal Pyramid F = 7 V = 7 E = 12 Use Euler's Theorem to find the value of n. 3. Faces: n Vertices: 4 Edges: 6 n + 4 = 6 + 2 n = 4 4. Faces: 12 Vertices: 22 Edges: n 12 + 22 = n + 2 n = 32 5. Faces: 10 Vertices: n Edges: 24 10 + n = 24 + 2 n = 16 6. Find the surface area of the solid formed by the net. [Image of a net forming a cylinder] r = 5, h = 6 SA = 2πr² + 2πrh = 2π(5)² + 2π(5)(6) = 50π + 60π = 110π ≈ 345.58 Find the surface area AND volume of the following figures. Assume all prisms, cylinders, and cones to be right and all pyramids to be regular. 7. EXACT! (SA) [Image of a sphere with radius 5] SA = 4πr² = 4π(5)² = 100π ≈ 314.16 V = (4/3)πr³ = (4/3)π(5)³ = 523.6π ≈ 1633.62 8. EXACT! [Image of a cone with radius 5 and height √39] SA = πr² + πrℓ = π(5)² + π(5)(8) = 25π + 40π = 65π ≈ 204.20 V = (1/3)πr²h = (1/3)π(5)²(√39) ≈ 52.04π ≈ 163.49 9. EXACT! [Image of a cylinder with radius 7 and height 5.11] SA = 2πr² + 2πrh = 2π(7)² + 2π(7)(5.11) = 98π + 71.54π = 169.54π ≈ 533.34 V = πr²h = π(7)²(5.11) = 249.97π ≈ 785.16 10. EXACT! [Image of a triangular pyramid with base side length 12 and height 28] B = (1/2)(12)(12√3) B = 72√3 P = 36 h = 28 SA = 72√3 + (1/2)(36)(28) SA = 72√3 + 504 SA ≈ 633.05 + 504 ≈ 1137.05 V = (1/3)(72√3)(28) V = 704√3 ≈ 1218 11. EXACT! [Image of a square pyramid with base side length 7 and slant height 10] B = 7² = 49 P = 28 ℓ = 10 SA = 49 + (1/2)(28)(10) SA = 49 + 140 SA = 189 V = (1/3)(49)(7) V = 343/3 ≈ 114.33 12. EXACT! (VOL) [Image of a cone with radius 9.93 and height 21.42] r = 9.93 9.93² + 21.42² = ℓ² ℓ ≈ 23.61 SA = π(9.93)² + π(9.93)(23.61) SA ≈ 98.69π + 234.4π SA ≈ 333.09π ≈ 1046.30 V = (1/3)π(9.93)²(21.42) V ≈ 704.04π ≈ 2211.8 13. EXACT! (VOL) [Image of a triangular pyramid with base side length 8 and height 5] B = (1/2)(8)(8√3) B = 32√3 P = 24 ℓ = 5 SA = 32√3 + (1/2)(24)(5) SA = 32√3 + 60 SA ≈ 55.43 + 60 ≈ 115.43 V = (1/3)(32√3)(5) V = 160√3/3 ≈ 92.38 14. [Image of a cylinder with radius 46.25 and height 44.25] r = 46.25 SA = 2π(46.25)² + 2π(46.25)(44.25) SA ≈ 13440.13 + 12868.93 SA ≈ 26299.06 V = π(46.25)²(44.25) V ≈ 297362.79 15. EXACT! (SA) [Image of a hemisphere with radius 10.35] r = 10.35 SA = 2πr² SA = 2π(10.35)² SA ≈ 673.07 V = (2/3)πr³ V = (2/3)π(10.35)³ V ≈ 2322.09 16. EXACT! [Image of a cone with radius 9.93 and height 21.42] r = 9.93 9.93² + 21.42² = ℓ² ℓ ≈ 23.61 SA = π(9.93)² + π(9.93)(23.61) SA ≈ 98.69π + 234.4π SA ≈ 333.09π ≈ 1046.30 V = (1/3)π(9.93)²(21.42) V ≈ 704.04π ≈ 2211.8 17. EXACT! [Image of a sphere with radius √14] r = √14 SA = 4πr² SA = 4π(√14)² SA = 56π V = (4/3)πr³ V = (4/3)π(√14)³ V = (56/3)π√14 18. EXACT! [Image of a triangular pyramid with base side length 8 and height 5] B = (1/2)(8)(8√3) B = 32√3 P = 24 ℓ = 5 SA = 32√3 + (1/2)(24)(5) SA = 32√3 + 60 SA ≈ 55.43 + 60 ≈ 115.43 V = (1/3)(32√3)(5) V = 160√3/3 ≈ 92.38