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**Surface area and Volume Good luck. No work=No credit.**

Name: Period: 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.

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**Part 1: Matching 1.)prism A.) Type of solid. 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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**Sample problem for 1 and 2: Find the volume and total area of a cube with edge 2k.**

Volume=Bh =(2k2k)(2k) =8k3 units3 Total Area=LA+2B =ph+2B =8k(2k)+2(2k)(2k) =16k2+8k2 =24k2 units2 2k 2k 2k 2k 2k 2k 2k

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**1.) Find the volume of this rectangular prism**

10 Bases 4 3

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

10 Bases 4 3

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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) =600+60 =660 units2 20cm 13cm 5cm 12cm

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**Sample problem A right triangular prism has height 10 and base edges 3, 4, 5. TA?**

Total area=_______ 10cm 5cm 3cm 4cm

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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 units2 12 8 8 6

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**4. Find Lateral Area of the triangular prism**

20 16 16 12

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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) p=20 ml

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**Find the missing variable for each prism.**

7.) LA=729 p= h=9

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**Sample problem: Find the volume of a Cylinder**

√H = √9 H = 3 V=Bh =πr2h =π(2)2(3) =12π ft.3 5 ft h=___ ft 4 ft d=______ r=______ h=______

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**8. Find the volume of a Cylinder**

25 ft h=___ ft 24 ft d=______ r=______ h=______

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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? 12:22 = 1:4 c.) Ratio of volumes? 13:23 = 1:8 If the volume of the smaller cylinder is 48 cm3 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 cm3 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 b.) Volume= =4π(10)2 =4π(100) =400π cm2

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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 135cm3 Find h.**

Volume=1/3Bh 135=1/3(9)h 135= 3h 45 cm=h h 3 cm 3 cm

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**11. A regular pyramid has a base edge of 3cm and volume 100cm3 Find h.**

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**Sample problem A cone has radius 8 and height 6. Find the volume**

Sample problem A cone has radius 8 and height 6. Find the volume. Slant height V=1/3Bh =1/3πr2h =1/3π(8)2(6) =1/3π64(6) =1/3π384 =384/3π =128π L=slant height 62+82=l2 36+64=l2 100=l2 10=l (2x3)2+(2x4)2=l2 l=5x2=10 H=6 r=8

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**12. A cone has radius 12 and height 9. Find the volume. Slant height**

L=slant height =__________ H=9 r=12

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**Sample problem A cone has radius 8 and height 6. Find Total area.**

TA=LA+B =πrl+πr2 =π(8)(10)+π82 =80π+64π =144π units2 l=slant height 62+82=l2 36+64=l2 100=l2 10=l (2x3)2+(2x4)2=l2 l=5x2=10 H=6 r=8

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**13. A cone has radius 12 and height 9. Find Total area.**

l=slant height =_____ H=9 r=12

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**Sample problem A cylinder has a radius 6cm and height 4cm**

Sample problem A cylinder has a radius 6cm and height 4cm. Find total area. TA=LA+2B =ph+2B =(2πr)h+2πr2 =2π(6)(4)+2π62 =48π+72π =120π cm2 h=4 R=6

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**14. A cylinder has a radius 8cm and height 3cm. Find total area.**

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**Sample problem. A cylinder has a radius 6cm and height 4cm. Find volume.**

V=Bh =πr2h =π62(4) =π36(4) =144π cm3 h=4 R=6

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**15. A cylinder has a radius 8cm and height 3cm. Find volume.**

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Lateral Area, Surface Area and Volume

Lateral Area, Surface Area and Volume

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