In Problems #1 - #4, find the surface area and volume of each prism.

Transcription

1 Geometry Unit Seven: Surface Area & Volume, Practice In Problems #1 - #4, find the surface area and volume of each prism. 1. CUBE. RECTANGULAR PRISM 9 cm 5 mm 11 mm mm 9 cm 9 cm. TRIANGULAR PRISM 4. TRIANGULAR PRISM 16 in 10 ft 14.5 ft 9 in 0 in 6 ft 5. A rectangular prism has a surface area of 448 cm. Its length is 14 cm and its width is 6 cm. Find its height. 6. A cylinder has a radius of 1 cm and a height of 15 cm. Find its surface area and volume. Express your answer in 7. A cylinder has a diameter of 10 in and a height of 5 in. Find its surface area and volume. Express your answer in 8. A cylinder has a radius of 7.5 mm and a height of 1.5 mm. Find its surface area and volume. Express your answer in

2 In Problems #9 - #1, find the volume of each pyramid cm 7 cm 8 mm 1 mm 7 cm 1 mm A pyramid has a hexagon for its base. Each edge of the base is 15 feet, and the height of the pyramid is 10 feet. 4 in 5 in 5 in 1. Find the volume of a cone has a radius of 1 cm and a height of 0 cm. Express your answer in 14. Find the volume of a cone has a diameter of 4 mm and a height of 15 mm. Express your answer in 15. Find the volume of a cone has a radius of 16 in and a height of 19 in. Express your answer in 16. A cone has a volume of 11π cm and a height of 1 cm. Find its radius.

3 17. A sphere has a radius of 4 cm. Find its surface area and its volume. Express your answer in 18. A sphere has a diameter of feet. Find its surface area and its volume. Express your answer in 19. A sphere has a radius of 8 mm. Find its surface area and its volume. Express your answer in 0. A sphere with a diameter of 0 inches is placed in a cube. The sphere touches the lateral faces and the bases of the cube. Find the dimensions of the cube, the volume of the cube, the volume of the sphere, and the volume inside the cube that is not taken up by the sphere. ******************************ANSWERS****************************** 1) Area of each face = 9 cm 9 cm = 81 cm ; Surface area of cube = 6 81 cm = 486 cm Volume = Area of Base Height V = B h Area of base = 9 cm 9 cm = 81 cm V = 81 cm 9 cm = 79 cm ) Area of front & back face = 11 mm 5 mm = 55 mm ; Area of top & bottom faces = 11 mm mm = mm ; Area of left & right faces = mm 5 mm = 15 mm ; Surface area of prism = 55 mm + mm + 15 mm = 06 mm Volume = Area of Base Height V = B h Area of base = 11 mm mm = mm V = mm 5 mm = 165 mm ) Find missing side using Pythagorean Theorem = x = x 1156 = x 1156 = x 4 = x Area of front & back faces = 1/ 0 in 16 in = 40 in Area of bottom face = 0 in 9 in = 70 in 16 in Area of left face = 16 in 9 in = 144 in Area of top diagonal face = 4 in 9 in = 06 in Surface area = 40 in + 70 in in + 06 in = 100 in x 0 in 9 in Since this is a triangular prism, the base of the figure is a triangle, and the height of the figure is 9 in Volume = Area of Base Height V = B h Area of base = 1/ 0 in 16 in = 40 in V = 40 in 9 in = 160 in

4 4) Find missing side using Pythagorean Theorem x = x = 10.5 x = x = x= 10.5 Area of front & back faces = 1/ 10 ft 10.5 ft = 5.5 ft Area of bottom face = 10.5 ft 6 ft = 6 ft Area of left face = 10 ft 6 ft = 60 ft Area of top diagonal face = 14.5 ft 6 ft = 87 ft Surface area = 5.5 ft + 6 ft + 60 ft + 87 ft = 15 ft 10 ft 14.5 ft Since this is a triangular prism, the base of the figure is a triangle, and the height of the figure is 6 ft Volume = Area of Base Height V = B h Area of base = 1/ 10 ft 10.5 ft = 5.5 ft V = 5.5 ft 6 ft = 15 ft x 6 ft 5) Area of front & back faces = 14 cm x cm = 14 x cm ; Area of top & bottom faces = 14 cm 6 cm = 84 cm Area of right & left faces = 6 cm x cm = 6 x cm Surface area = Front + Back + Top + Bottom + Right + Left 448 = 14x x 448 = 8x x 448 = 40x = 40x 7 cm = x 14 cm 6 cm x Area of top & bottom circles: π Radius = π 1 cm = 144 π cm 6) ( ) The length of the rectangular lateral area is equal to the circumference of the top & bottom circle Circumference = π Radius π 1 cm = 4 π cm Lateral area = 15 cm 4 π cm = 60 π cm Surface area = 144 π cm + 60 π cm 648 π cm cm 1 cm 15 cm 1 cm * PI * 1 cm Volume = Area of Base Height V = B h ( ) V Area of base = π 1 cm = 144 π cm = 144 π cm 15 cm = 160 π cm cm 7) Diameter of top & bottom circles = 10 in Radius = 10 in = 5 in ( ) Area of top & bottom circles: π Radius = π 5 in = 5 π in The length of the rectangular lateral area is equal to the circumference of the top & bottom circle Circumference = π Diameter π 10 in = 10 π in Lateral area = 5 in 10 π in = 50 π in Surface area = 5 π in + 50 π in 100 π in in 10 in 5 in 10 in PI * D Volume = Area of Base Height V = B h ( ) V Area of base = π 5 in = 5 π in = 5 π in 5 in = 15 π in 9.70 in

5 Area of top & bottom circles: π Radius = π 7.5 mm = 56.5 π mm 8) ( ) The length of the rectangular lateral area is equal to the circumference of the top & bottom circle Circumference = π Radius π 7.5 mm = 15 π mm Lateral area = 1.5 mm 15 π mm = π mm Surface area = 56.5 π mm π mm 00 π mm mm 7.5 mm 1.5 mm 7.5 mm * PI * R ( ) Volume = Area of Base Height V = B h Area of base = π 7.5 mm = 56.5 π mm V = 56.5 π mm 1.5 mm = π mm 08.9 mm 9) Volume 1/ Area of Base Height 1/ Area of base 7 cm 7 cm 49 cm = V = B h = = V = 1/ 49 cm 6 cm = 98 cm 10) Volume = 1/ Area of Base Height V = 1/ B h Area of base = 1 mm 1 mm = 144 mm V = 1/ 144 mm 8 cm = 84 mm 11) Volume 1/ Area of Base Height V 1/ B h Area of base 5 in 5 in 5 in = = = = 1 V = 1/ 5 in 4 in = in. in 1) Volume = 1/ Area of Base Height V = 1/ B h ( ) V Area of base = / 15 ft = 7.5 ft = 1/ 7.5 ft *10 ft V = 115 ft ft 1) ( ) Volume = 1/ Area of Base Height V = 1/ B h Area of base = π 1 cm = 144 π cm V = 1/ 144 π cm 0 cm = 960 π cm cm 14) If diameter of cone = 4 mm, then radius of cone = 1 mm Volume = 1/ Area of Base Height V = 1/ B h ( ) π Area of base = π 1 mm = 144 mm V = 1/ 144 π mm 15 mm V = 70 π mm mm 15) ( ) Volume = 1/ Area of Base Height V = 1/ B h Area of base = π 16 in = 56 π in 1 V = 1/ 56 π in 19 in = 161 π in 161. π in in

6 16) ( ) π Volume = 1/ Area of Base Height V = 1/ B h Area of base = π r cm = r cm ( ) ( ) V = 1/ B h 11π = 1/ π r 1 Multiply both sides by 6π = π r 1 Divide both sides by 1 16π π Divide both sides by π cm = r = r = r = r 17) SA ( ) Surface Area = 4 π Radius = 4 π 4 cm SA = 04 π cm 78. cm ( ) Volume = 4/ π Radius V = 4/ π 4 cm V = 184 π cm cm 18) If a sphere has a diameter of feet, it has a radius of 1.5 feet. ( ) ( ) Surface Area = 4 π Radius SA = 4 π 1.5 ft SA = 9 π ft 8.7 ft Volume = 4/ π Radius V = 4/ π 1.5 ft V = 4.5 π ft ft Surface Area = 4 π Radius SA = 4 π 8 mm SA = 56 π mm mm 19) ( ) ( ) Volume 4/ π Radius V 4/ π 8 mm = = V = 68 π mm π mm mm 0) The dimensions of the cube are equal to the diameter of the sphere since the sphere touches all the faces of the cube Dimensions of cube = 0 in by 0 in by 0 in; Volume of Cube Area of Base Height V B h Area of base 0 in 0 in 900 in = = = = V = 900 in 0 in = 7000 in If a sphere has a diameter of feet, it has a radius of 1.5 feet. ( ) Volume of Sphere = 4/ π Radius V = 4/ π 15 in V = 4500 π in in Volume inside cube not taken up by sphere = 7000 in in = in