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Mensuration

Mensuration. Try this. 1. Consider the following situations. In each find out whether you need volume or area and why?. ( i ). Quantity of water inside a bottle. Here we need Volume 3-Dimension shape. ( ii ) Canvas need for making a tent.

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Mensuration

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  1. Mensuration Try this 1. Consider the following situations. In each find out whether you need volume or area and why? ( i ). Quantity of water inside a bottle Here we need Volume 3-Dimension shape ( ii ) Canvas need for making a tent Here we need area – Lateral Surface Area or Total Surfae Area ( iii ) Number of bags inside the lorry Here we need Volume 3-Dimension shape ( iv ) Gas filled in a cylinder Here we need Volume 3-Dimension shape ( v ) Number of match sticks that can be put in the match box Here we need Volume 3-Dimension shape

  2. Try this Compute 5 more such examples and ask your friends to choose what they need ? ( i ) Quantity of Ice cream in Ice Cream Cone ( ii ) Quantity of Whitewash required to whitewash the wallls of room ( iii ) Quatity of rice bags in a heap of rice ( iv ) Quantity of water required to store in a steel pot ( v ) Number of Cloths to store in a suitcase

  3. Try this 1.Break the pictures in the following figures into Solids of Known shapes Cylinder , Hemisphere Cubiod, cylinder Cuboid, Cylinder Sphere, Cylinder Sphere,Sphere Cylinder , Cylinder Sphere Cylinder , Cone , Cone

  4. Try this 2. Think of 5 more things around you that can be seen as a Combination of shapes. Name the shapes that combine to make them . Ring Cuboid Cylinder Cylinder Sphere Hemisphere Cuboid Sphere Cylinder Cuboid Cuboid Cylinder

  5. Try this 2. Think of 5 more things around you that can be seen as a Combination of shapes. Name the shapes that combine to make them .

  6. Figure Lateral / Curved Surface area Total Surface Area Noman Clature Volume Name of the Solid l : length b:breadth h: height lbh Cuboid 2h ( l+b ) 2(lb+bh+hl ) Cube 4a2 6a2 a3 a : side of the cube Lateral Surfave area +2(area of the end Surface) Right Prism Area of base x height Perimeter of base x height r: radius of the base h: height Regular Circular Cylinder Lateral Surface area + area of the base (area of the base ) X height (perimeter of base ) x Slant height Right Pyramid Right Circular cone r : radius of base h: height l : Slant height Sphere r : radius r : radius Hemisphere

  7. Example:1 The radius of a conical tent is 7 meters and its height is 10 meters . Calculate the length of canvas used in making the tent if width of convas is 2 meters . Solution:Radius of of conical tent Height Slant height of the conical Tent Lateral Surface Area of conical Tent Area of the canvas used in making the tent Breadth of canvas Area of the canvas = length of canvas X breadth of the canvas 268.4 = length of the canvas x 2 Length of the canvas

  8. Example : 2 An Oil drum is in the shape of a cylinder having the following dimensions . Diameter is 2 m. and height is 7 meters . The painter charges Rs.3 per m2 to paint the drum . Find the total charges to be paid to the painter for 10 drums . Solution : It is given that diameter of the cylinderical oil drum = 2m 7 m Radius of cylinder = r = d / 2 = 2 / 2 = 1m Height of the Oil drum = h = 7 m 1m Total surface area of the cylinderical oil drum = The painter charges Rs.3 per 1 Sq. m Total charges to be paid to the painter for 1 drum = 3x50.28 = Rs.150.84 Total charges to be paid to the painter for 10 drums = 10x150.84 = Rs.1508.40

  9. Example : 3 A sphere , a cylinder and a cone are of the same radius and same height . Find the ratio of their curved surface areas ? Solution : Let r be the common radius of a sphere , a cone and a cylinder Height of the sphere (h) = Diameter of the sphere = 2r The height of the cone = height of cylinder = height of sphere = 2r Slant height of the cone S1 = Curved Surface Area of Sphere = S2 = Curved surface Area of the cylinder S3 = Curved Surface Area of Cone Ratio of curved Surface area as

  10. Example : 4 A company wanted to manufacture 1000 hemispherical basins from a thin steel sheet . If the radius of hemispherical basins is 21 cm. Find the required area of steel sheet to manufacture the above hemispherical basins ? Solution : Radius of the hemispherical basin Lateral Surface area of hemishperical basin The steel sheet required for on e basin Total area of steel sheet required for 1000 basins

  11. Example : 5 A right circular cylinder has base radius 14 cm and height 21 cm. Find (i) Area of base or area of each end (ii) Curved Surface area (iii) Total Surface area and (iv) Volume of the right circular cylinder Solution : Radius of the cylinder Height of the cylinder (i) Area of base or area of each end of cylinder (ii) Curved Surface area of the right circular cylinder (iii) Total Surface area of the right circular cylinder area of the base Curved Surface area (iv) Volume of the right circular cylinder = Area of the base X height

  12. Example : 6 Find the volume and Surface area of a sphere of radius 2.1 cm Solution : Radius of Sphere Surface area of sphere Volume of sphere

  13. Example : 7 Find the Volume and the total Surface area of a hemisphere of radius 3.5 cm . Solution : Radius of hemisphere Total Surface area of hemisphere Volume of hemisphere

  14. Exercise - 10.1 1. A Joker’s cap is in the form of right circular cone whose base radius is 7 cm and height is 24 cm . Find the area of the sheet required to make 10 such caps . Solution : base radius of the right circular cone shape Joker’s cap Height Slant height of cone The area of the sheet require to make one cap = Curved surface area of the right circular cone The area of the sheet require to make 10 such caps

  15. Exercise - 10.1 2. A sports company was ordered to prepare 100 Paper cylinders for shuttle cocks. The required dimensions of the cylinder are 35 cm length / height and its radius is 7 cm. Find the required area of thin paper sheet needed to make 100 cylinders ? Solution : Radius of the cylinder Height Required area of thin paper sheet needed to make one cylinder = The Total Surface area of the Cylinder Required area of thin paper sheet needed to make 100 cylinders

  16. Exercise – 10.1 3. Find the volume of right circular cone with radius 6 cm and height 7 cm. Solution : Radius of right circular cone Height volume of right circular cone

  17. Exercise - 10.1 4. The lateral surface area of a cylinder is equal to the curved surved surface area of a cone . If the radius be the same . Find the ratio of the height of the cylinder and slant height of the cone . Solution : The radius of cylinder and cone be same . Let r. Let height of the cylinder be h and slant height of the cone be l Lateral surface area of the cylinder = Curved surface area of the cone The lateral surface area of a cylinder is equal to the curved surved surface area of a cone .

  18. Exercise - 10.1 5. A Self help group wants to manufacture joker’s cap ( Conical caps) of 3cm radius and 4 cm height . If the available color paper sheet is 1000 cm2 , then how many caps can be manufactured from that paper sheet ? Solution: Radius of Joker,s cap ( Conical cap ) Height Slant height = Curved Surface area of conical Cap Colour paper required to manufacture one Joker;s conical cap = 47.14cm2 Number of caps can be manufactured from 1000 cm2 colour paper sheet

  19. Exercise - 10.1 6. A Cylinder and cone have bases of equal radii and arc of equal heights . Show that their volumes are in the ratio of 3:1 Solution : Given that a cylinder and cone have bases of equal radii Let radii is r Also given that a cylinder and cone have equal heights. Let heights be h Volume of a cylinder = Volume of a cone = The ratio of their volumes

  20. Exercise - 10.1 7. A Solid Iron rod has a cylinderical shape. Its height is 11 cm and base diameter is 7 cm . Then find the total volume of 50 rods ? Solution : Height of the cylinderical shape Solid Iron rod Base diameter of a cylinderical shape solid Iron rod Radius of Cylinderical shape solid Iron rod Volume of cylinderical shape solid Iron rod = Volume of 50 cylinderical shape solid Iron rods =

  21. Exercise - 10.1 8. A heap of rice is in the form of a cone of diameter 12 m and height 8 m . Find its volume ? How much canvas cloth is required to cover the heap ? Solution : diameter of a heap of rice which is in the form of cone Radius Height of a heap of rice Slant height Volume of a heap of rice = Lateral Surface area of the heap of rice which is in the form of cone

  22. Exercise - 10.1 9. The curved surface area of a cone is 4070 cm2 and its diameter is 70 cm . What is its slant height ? Solution : diameter of a cone Radius Let Slant height of the cone be l Curved surface area of cone

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