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Last updated at May 29, 2018 by Teachoo
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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 = 18 cm Height = h = 32 cm Volume of cylindrical bucket = ๐r2h = ๐ (18)2 32 = ๐ ร 18 ร 18 ร 32 Volume of conical heap Height = h = 24 cm Let Radius = ๐ cm & Slant height = l cm Volume of conical heap = 1/3 ๐r2h = 1/3 ๐r2 24 = 8๐r2 Now, Volume of cylindrical bucket = Volume of conical heap ๐ ร 18 ร 18 ร 32 = 8๐r2 (๐ ร 18 ร 18 ร 32)/8๐ = r2 r2 = (๐ ร 18 ร 18 ร 32)/8๐ r2 = 18ร18ร 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 = โ1872 l = โ(12 ร12 ร13) l = โ(ใ12ใ^2 ร13) l = โ(ใ12ใ^2 ) ร โ13 l = 12โ13 cm
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