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Ex 13.3, 7 - A cylindrical bucket, 32 cm high and radius - Conversion of one shape to another

  1. Chapter 13 Class 10 Surface Areas and Volumes
  2. Serial order wise
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Ex 13.3, 7 A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap. Since sand in cylindrical bucket is emptied to make a conical heap Volume of cylindrical bucket = volume of conical heap Volume of cylindrical bucket Radius = ๐‘Ÿ = 18 cm Height = h = 32 cm Volume of cylindrical bucket = ๐œ‹r2h = ๐œ‹ (18)2 32 = ๐œ‹ ร— 18 ร— 18 ร— 32 Volume of conical heap Height = h = 24 cm Let Radius = ๐‘Ÿ cm & Slant height = l cm Volume of conical heap = 1/3 ๐œ‹r2h = 1/3 ๐œ‹r2 24 = 8๐œ‹r2 Now, Volume of cylindrical bucket = Volume of conical heap ๐œ‹ ร— 18 ร— 18 ร— 32 = 8๐œ‹r2 (๐œ‹ ร— 18 ร— 18 ร— 32)/8๐œ‹ = r2 r2 = (๐œ‹ ร— 18 ร— 18 ร— 32)/8๐œ‹ r2 = 18ร—18ร— 4 r2 = 182 ร— 22 r2 = (18 ร— 2)2 r2 = 362 r = 36 cm Now , we have to find slant height (l) We know that l2 = h2 + r2 l2 = 242 + 362 l2 = 576 + 1296 l2 = 1872 l = โˆš1872 l = โˆš(12 ร—12 ร—13) l = โˆš(ใ€–12ใ€—^2 ร—13) l = โˆš(ใ€–12ใ€—^2 ) ร— โˆš13 l = 12โˆš13 cm

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