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WELCOME

WELCOME. WELCOME. Surface Areas and Volumes. By. N.Vinay Chowdary IX- 'A'. Surface Area of a Cuboid. D. C. A. B. h. H. l. b. G. E. F.

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WELCOME

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  1. WELCOME WELCOME

  2. Surface Areas and Volumes By N.Vinay Chowdary IX- 'A'

  3. Surface Area of a Cuboid D C A B h H l b G E F The surface of a cuboid consists of six rectangular faces. So, the surface area of a cuboid equals the sum of the areas of its six rectangular faces. Procedure to derive the formula for the surface area of a cuboid is as follows :

  4. Procedure • Consider a cuboid whose length is l cm, breadth b cm and height h cm as shown in the above figure. • Area of face ABCD = Area of face EFGH = (l x b) cm2. • Area of face AEHD = Area of face BFGC = (b x h) cm2. • Area of face ABFE = Area of face DHGC = (l x h) cm2. Therefore, total surface area of the cuboid = Sum of the areas of all its six faces = 2(l x b) + 2(b x h) + 2(l x h) cm2 = 2(l x b + b x h + l x h) cm2 = 2(lb + bh + lh) cm2 = 2(length x breadth + breadth x height + length x height) cm2

  5. Surface Area of a Cube Since all the six faces of a cube are squares of the same size i.e. for a cube we have l=b=h. Thus, if 1 cm is the length of the edge or side or a cube, then ; Surface area of the cube = 2(l x l + l x l + l x l) = 2 x 3l2 = 6l2 = 6(Edge)2

  6. Questions & Answers

  7. Q. 1 :Three equal cubs are placed adjacently in a row. Find the ratio of total surface area of the new cuboids to that of sum of the surface areas of the three cubes? (Ans)

  8. Q. 2 : The diameter of a sphere is decreased by 50%. What is the ratio between initial and final curved surface areas? Ans:

  9. Q. 3 : Find the volume of the largest right circular cone that can be fitted in a cube whose edge is 14cm? Ans:

  10. Q. 4 : A plastic box 1.25 m long,1.05 m wide and 75cm deep is to be made. It is to be open at the top. Ignoring the thickness of the plastic sheet, determine the area of the sheet required for making the box and also find the cost of sheet for it, if a sheet measuring 1sq.m. cost Rs. 20 ? Ans:

  11. Q. 5 : A reservoir is in the form of rectangular parallelepiped. Its length is 20 m . If 18kl of water is removed from the reservoir, the water level goes down by 15cm. Find the width of the reservoir? Ans:

  12. Q. 6 : How many litres of water flow out of a pipe having an area of cross-section of 5 Sq. cm. in one minute if the speed of the water in the pipe is 30cm/sec? Ans:

  13. Q. 7 : An open box is made of wood 3cm thick. Its external length, breadth and height are 1.48m,1.16m and 8.3dm. Find the cost of painting the inner surface of Rs. 50 per sq metre? Ans:

  14. Q. 8 : A wood toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is 6cm and its height is 4cm. Find the cost of painting the toy at the rate of Rs. 5 per 1000 sq.cm ? Ans:

  15. Q. 9 : A pendulum swings through an angle of 30 degree and describes an arc of length 7.7cm. Find the length of the pendulum? Ans:

  16. Q. 10 : Find the length of the arc, the area of the sector of a circle and the area of segment of the circle, if the radius of the circle is 28cm and the angle of the sector is 60 degree? Ans:

  17. Q. 11 : The semi-circular sheet of metal of diameter 28cm is bent into an open conical cup. Find the depth and the capacity of cup? Ans: To calculate the depth of cone = sqrt(h2-r2)

  18. Q. 12 : If V is the volume of a cuboid of dimension a,b,c and S is its surface area, then prove that Ans:

  19. Q. 13 : If two circular cylinders of equal volume have their height in the ratio 1:4, find the ratio of their radii? Ans:

  20. Q. 14 : A circular tent is cylindrical to a height of 3 metres and conical above it. If its diameter is 105m and the slant height of the conical portion is 53m, calculate the length of canvas 5m wide to make the required tent? Ans:

  21. Q. 15 : A wall of the length 10m was to be built across an open ground. The height of the wall is 4 m and thickness of the wall is 24cm. If this wall is to be built up with bricks whose dimensions are 24cmx12cmx8cm, how many bricks would be required? Ans:

  22. Q. 16 : Three metal cubes whose edges measure 3cm,4cm and 5cm respectively are melted to form a single cube. Find the edge of the new cube. Also find the surface area? Ans:

  23. THANKS

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