Solid Geometry

SOLID GEOMETRY CUBOID: Let length=l, breadth=b and height=h units. Then, Volume=(l*b*h) cubic units Surface area=2(lb+bh+hl) squints Length of longest diagonal =√ (l² + b² +h²). CUBE: let each edge of a cube be of length ‘a’. Then, Volume =a*a*a cubic units Surface area =6(a*a) squints Length of longest diagonal =√3 a. CYLINDER: let radius of base= r &height =h Then, Volume=3.14(r*r) h cubic units Curved Surface area= 6(a*a) CONE: Let radius of base=r & height = h. Then, Slant height, l = sq root [(h*h)+(r*r)] Volume = 1/3 [3.14*(r*r)*h] Curved Surface area = 2*3.14*r*l sq. units SRHERE: Let the radius of the sphere be ‘r’. Then, Volume = 4/3 * 3.14 (r*r*r) cubic units Surface area = 4*3.14*(r*r) sq. units PROBLEMS 1. Three cubes of sides’ 1cm, 6cm and 8cm are merged into one cube without leaving any space. What is the length of side of new cube? Also its surface area 2. If the volume and total curved surface area of a cube are same then what is the measure of side of the cube? 3. A road roller of diameter 3.5 m has to press a ground of area 1100sq meter. How many revolutions should it make? 4. Find the volume of the cube if the area of one of the faces is 81sqm? 5. The volume of a box with a square base is 128cc. The height of the box is twice the breadth of the box. Find the height? 6. If a cylindrical tank of diameter 14cm and of height 9cmis to be filled by water to 2/3rd of its height then what is the volume of the cylinder that is left empty? 7. Three cylindrical tanks of diameters 2m, 4m and 8m and of same height are to be filled simultaneously. What is the ratio of time taken in which they are filled?

8. If a rectangular solid has sides of length 10m, 12m and of height 4m. What is the total curved surface area? 9.

Find the volume and surface area of the sphere if radius is 8.4m?

10. Find the number of balls of 2m diameters that can be made of a solid cylinder of diameter 14m and a height of 8m? 11. Find the slant height and curved surface area of a cone if the radius and height are 28m and 14m respectively? 12. If the heights of two cones are in the ratio of 3:4 and radii are in the ratio of 3:2, then their volumes are in the ratio of? 13. A river of 2m deep and 20m wide is flowing at a rate 5.4kmph.The amount of water that flows into the ocean in 3 minutes is? 14. Find the number of cubes of side 2m that can be accommodated in a cube of side 50m? 15. The three sides of a rectangular room are 3m, 4m, and 7m. Find the length of the longest diagonal? 16. The radius of a right circular cylinder is increased by 40%. Find the percentage increase in volume? 17. Find the volume of the largest circular cone that can be cut out of a cube of side 6 m? 18. The diameter of the circular building is 14m, which is 33m in height. The staircase has been built along the curved surface in such a way that the first step and the last step are in vertical line. Find the length of the staircase? 19. The length of the wire of diameter 0.4m made out of a solid sphere of radius 6m is? 20. If the height of cone is decreased by 64% then by what percent should the radius be raised to keep its volume same?