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Grade 8 Volume 1

Grade 8 Volume 1. 1. Solid Geometry. Solid geometry is concerned with three-dimensional shapes. Some examples of three-dimensional shapes are cubes, rectangular solids, prisms, cylinders, spheres, cones and pyramids.

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Grade 8 Volume 1

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  1. Grade 8 Volume 1 1 CONFIDENTIAL

  2. Solid Geometry Solid geometry is concerned with three-dimensional shapes. Some examples of three-dimensional shapes are cubes, rectangular solids, prisms, cylinders, spheres, cones and pyramids. The three flat shapes of the triangle, rectangle, and circle may become solids by adding the third dimension  of  depth. The  triangle  becomes  a  cone;  the  rectangle,  a  rectangular  solid;  and  the circle, a cylinder.

  3. s h w s s l Cubes A cube is a three-dimensional figure with all edges of the same length. If s is the length of sides of the cube, Volume of the cube = s3 Cuboids If l is the length, w is the width and h is the height of the cuboids, Volume of the cuboids = lbh

  4. r h r Cylinders A cylinder is a solid with two congruent circles joined by a curved surface. In the given figure, the radius of the circular base is r and the height is h. The volume of the cylinder is the area of the base × height. The volume of the cylinder =Πr2h. Spheres A sphere is a solid with all its points the same distance from the center. If r is the length of radius of the sphere, Volume of the sphere = 4Πr3 3

  5. h r Cones A circular cone has a circular base, which is connected by a curved surface to its vertex. A cone is called a right circular cone, if the line from the vertex of the cone to the center of its base is perpendicular to the base. . If r is the radius and h is the height, Volume of the cone= 1Πr2h 3

  6. s h b b Regular square pyramid Volume of theRegular square pyramid= 1b2h 3

  7. Let us do some practice problems!

  8. 1) What is volume of the cube with length of sides = 7 cm? • 343cm3 • 345cm3 • 347cm3 • 349cm3 a) 343cm3 CONFIDENTIAL 8

  9. 2) What is the volume of the cuboidwith length 7 cm, width4 cm and height6 cm. • 162cm3 • 164cm3 • 166cm3 • 168cm3 d) 168cm3 9 CONFIDENTIAL

  10. 8cm 10cm 3) What is the volume of the cylinder with radius of the base is 8 cm and the height is 10 cm? • 2008.6cm3 • 2019.6cm3 • 2009.6cm3 • 2109.6cm3 c) 2009.6cm3 10 CONFIDENTIAL

  11. A B C 3ft 2ft 2ft 6ft 1ft 3ft 2ft 3ft 4ft 4) Which of the given boxes has thegreatest volume? • Box A • Box B • Box C • All have equal volume b) Box B 11 CONFIDENTIAL

  12. 5) This net can be folded on the dashed lines to make a box. What is the volumeof the box? • 370 in3. • 270 in3. • 360 in3. • 250 in3. b) 270 in3 12 CONFIDENTIAL

  13. 6cm 6) What is the volume of the spherewith radius = 6 cm? • 904.32cm3 • 906.32cm3 • 908.32cm3 • 910.32cm3 a) 904.32cm3 CONFIDENTIAL

  14. 12 6cm 7) What isthe volume of the conewith radius 6 cm and the height is = 12 cm? (Use Π = 3.14) • 442.16 cm3 • 432.16 cm3 • 462.16 cm3 • 452.16 cm3 d) 452.16 cm3 14 CONFIDENTIAL

  15. 8) The rectangular prism at the right is made from centimeter cubes. What is the volume of the prism? • 88 cm3 • 64 cm3 • 48 cm3 • 76 cm3 c) 48 cm3 15 CONFIDENTIAL

  16. 12cm 11cm 11cm 9) What isthevolume of the regular squarepyramidwith base 11 cmand the height 12 cm? • 481 cm3 • 483 cm3 • 482 cm3 • 484 cm3 d) 484 cm3 16 CONFIDENTIAL

  17. 30 12.4cm 10) What is the volume of a cone, if the diameter of the cone is 12.4 cm. and the height of the cone is 30 cm ? (Use Π = 3.14) • 1205 cm3 • 1206 cm3 • 1207 cm3 • 1208 cm3 c) 1207 cm3 17 CONFIDENTIAL

  18. Assessment

  19. 1) A metal cube of edge 9 cm is melted and formed into 2 smaller cubes. If the edge of one smaller cube is 6 cm, what the side of the second smaller cube? • 6 cm • 4 cm • 7 cm • 8 cm d) 8 cm CONFIDENTIAL 19

  20. 2) Three cuboids of dimensions 2cm x 5cm x 7cm, 4cm x 4cm x 5cm and 2cm x 3cm x 11cm are melted and a cube is formed. What is theside of the cube? • 8 cm • 6 cm • 7 cm • 9 cm b) 6 cm 20 CONFIDENTIAL

  21. 10cm 13cm 3) What is the volume of the cylinder with radius of the base is 10 cm and the height is 13 cm? • 4082 cm3 • 4084 cm3 • 4086 cm3 • 4088 cm3 a) 4082 cm3 21 CONFIDENTIAL

  22. 4) What is the length of each edge of the box that is a perfect cube with volume512 units3? • 6 units • 5 units • 8 units • 7 units c) 8 units 22 CONFIDENTIAL

  23. 5) What isthevolumeof the given rectangular pyramid? • 892 cm3 • 972 cm3 • 794 cm3 • 772cm3 b) 972cm3 23 CONFIDENTIAL

  24. 13cm 6) What is the volume of the spherewith radius = 13 cm? • 9138.1 cm3 • 9158.1 cm3 • 9178.1 cm3 • 9198.1 cm3 d) 9198.1 cm3 24 CONFIDENTIAL

  25. A B C 4ft 4ft 3ft 5ft 3ft 4ft 3ft 4ft 5ft 7) Which of the given boxes has theleast volume? • Box A • Box B • Box C • All have equal volume a) Box A 25 CONFIDENTIAL

  26. 9 5 cm 8) What is the volume of the conewith radius 5 cm and the height is = 9 cm? • 235.5 cm3 • 232.5 cm3 • 237.5 cm3 • 231.5 cm3 a) 235.5 cm3 26 CONFIDENTIAL

  27. 9 cm 7cm 7cm 9) What isthe volume of the regular squarepyramidwith base 7 cmand the height 9 cm? • 143 cm3 • 145 cm3 • 147 cm3 • 149 cm3 c) 147 cm3 27 CONFIDENTIAL

  28. 10) What isthe volumeof the given box? • 42 cm3 • 52 cm3 • 92 cm3 • 102 cm3 a) 42 cm3 28 CONFIDENTIAL

  29. You did a great job today!

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