Geometry Practice Test

12.1 Prisms Find the (1) lateral area and (2) total area and (3) volume of the right prism (1) LA = pH LA = 600 (2) TA = LA + 2B TA = [(½)(5)(12)] TA = 660 LA = [ ] (20) base = ½(5)(12) (3) V = Bh TA = 30(20) TA = 600

12.2 Pyramids The lateral area of a regular pyramid with n lateral faces is n times the area of one lateral face Find the (4) lateral area of this regular pyramid. L.A. = nF 6 10 A = ½ b(h) A = 3(10) A = 30 LA = nF LA = 6(30) LA = 180 square units OR… The lateral area of a regular pyramid equals half the perimeter of the base times the slant height. L.A. = ½ pl LA = ½ pl LA = ½ 36(10) LA = 180 square units We have 6 triangles!

5) Find the total area of this regular pyramid. The total area of a pyramid is its lateral area plus the area of its base T.A. = L.A. + B That makes sense! A = ½ a(p) √3 A = ½ 3√3(36) A = 3√3(18) A = 54√3 TA = LA + B TA = √3 sq. units

12.3 Cylinders Find the (6) lateral area (7) height and (8) volume. (6) TA = LA + 2B 24π = LA + 2(4π) LA = 16π un² (7) LA = CH 16π = 4π H H = 4 un Base area = π 2² = 4π (8) V = πr²H V = 4π 4 = 16π un³ Base circumference = 2(2)π = 4π radius: 2 Total Area: 24  24π = LA + 8π

12.3 Cones radius: 5 Total Area: 90  cm 2 Volume: _____ Find the missing information.(9) Find l and h. (10) Find volume. (9) TA = πrl + B 65π = π(5)l l = 13 un h = 12 un (10) V = 1/3πr²h V = 1/3 π 5² 12 = 100π un³ π Base area = π 5² = 25π 90 π = π(5)l + 25 π

12.4 Spheres 11. area = 100π Volume: _____ Surface Area = Volume = 100π = 4πr 2 25 = r 2 r = 5

12. Find the area of a circle formed when a plane passes 5 cm from the center of a sphere with radius 8 cm. 5 8 √39 Area of the blue circle = 39π cm 2

HW Chapter Review P. 518 (1-15)