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Chapter 12 Test: Instructions: Leave all answers in terms of π and reduce all fractions. Surface area and Volume Good luck. No work=No credit. Name: Period:

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Part 1: Matching 1.)prism 2.)bases 3.)altitude 4.)lateral faces 5.)lateral edges 6.)right prism 7.)oblique prism A.) Type of solid. B.) Congruent polygons & //. C.) Faces, not including bases D.) Where adjacent lateral faces intersect in // segments. E.) Lateral faces not rectangles F.) Lateral faces are rectangles. G.) Segment _I_ to and joining two base planes.

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Volume=Bh =(2k2k)(2k) =8k 3 units 3 Total Area=LA+2B =ph+2B =8k(2k)+2(2k)(2k) =16k 2 +8k 2 =24k 2 units 2 Sample problem for 1 and 2: Find the volume and total area of a cube with edge 2k. 2k

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1.) Find the volume of this rectangular prism Bases

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2.) Find the Lateral area and Total area of this rectangular prism Bases

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Sample problem A right triangular prism has height 20 and base edges 5, 12, 13. Total area? TA=LA+2B =ph+2(1/2bh) =30(20)+2(1/2)(5)(12) = =660 units 2 5cm 13cm 12cm 20cm

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Sample problem A right triangular prism has height 10 and base edges 3, 4, 5. TA? Total area=_______ 3cm 5cm 4cm 10cm

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Sample problem for 4. Find the Lateral Area of a triangular prism LA=ph =(8+8+6)(12) =22(12) =264 units

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4. Find Lateral Area of the triangular prism

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Sample problem. Find the missing variable for each prism. 5.) B=9 in. 2 V=81 in. 3 h= 6.) V=121 B= h=11 7.) LA=180ml p= h=9ml V=Bh 81=9h h=9 in. 9 9 V=Bh 121=B(11) B=11 in LA=ph 180= p(9) 9 9 p=20 ml

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Find the missing variable for each prism. 5.) B=9 V=63 h= 6.) V=225 B= h=11 7.) LA=729 p= h=9

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Sample problem: Find the volume of a Cylinder h =5 2 h 2 +16= H 2 = 9 H = 3 V=Bh =πr 2 h =π(2) 2 (3) =12π ft. 3 5 ft 4 ft d=______ r=______ h=______ h=___ ft

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8. Find the volume of a Cylinder 25 ft 24 ft d=______ r=______ h=______ h=___ ft

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Sample problem: If the ratio of radii of two similar cylinders is 1:2 a.) Ratio of corresponding Perimeters? 1:2 b.) Ratio of areas? 1 2 :2 2 = 1:4 c.) Ratio of volumes? 1 3 :2 3 = 1:8 If the volume of the smaller cylinder is 48 cm 3 what is the volume of the bigger sphere?

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9.) If the ratio of radii of two similar cylinders is 3:5 a.) Ratio of corresponding Perimeters?_______ b.) Ratio of areas?______ c.) Ratio of volumes?______ If the volume of the smaller sphere is 54 cm 3 what is the volume of the bigger sphere?

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Sample Problem: Find the area and volume of the sphere with a radius of 10 cm a.) Area=4πr 2 b.) Volume= =4π(10) 2 =4π(100) =400π cm 2

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10. Find the area and volume of the sphere with a radius of 5 a.) Area=_______ b.) Volume=_______

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Sample problem A regular pyramid has a base edge of 3cm and volume 135cm 3 Find h. Volume=1/3Bh 135=1/3(9)h 135= 3h cm=h 3 cm h

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11. A regular pyramid has a base edge of 3cm and volume 100cm 3 Find h. h=________ 3 cm h

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Sample problem A cone has radius 8 and height 6. Find the volume. Slant height V=1/3Bh =1/3πr 2 h =1/3π(8) 2 (6) =1/3π64(6) =1/3π384 =384/3π =128π H=6 r=8 L=slant height =l =l 2 100=l 2 10=l (2x3) 2 +(2x4) 2 =l l=5x2=10

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12. A cone has radius 12 and height 9. Find the volume. Slant height V=_______ H=9 r=12 L=slant height =__________

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Sample problem A cone has radius 8 and height 6. Find Total area. H=6 r=8 l=slant height =l =l 2 100=l 2 10=l (2x3) 2 +(2x4) 2 =l l=5x2=10 TA=LA+B =πrl+πr 2 =π(8)(10)+π8 2 =80π+64π =144π units 2

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13. A cone has radius 12 and height 9. Find Total area. H=9 r=12 l=slant height =_____ TA=_______

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Sample problem A cylinder has a radius 6cm and height 4cm. Find total area. TA=LA+2B =ph+2B =(2πr)h+2πr 2 =2π(6)(4)+2π6 2 =48π+72π =120π cm 2 R=6 h=4

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14. A cylinder has a radius 8cm and height 3cm. Find total area. TA=_________ R=8 h=3

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Sample problem. A cylinder has a radius 6cm and height 4cm. Find volume. V=Bh =πr 2 h =π6 2 (4) =π36(4) =144π cm 3 R=6 h=4

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15. A cylinder has a radius 8cm and height 3cm. Find volume. V=________ R=8 h=3

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