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Acontainer shaped like a right circular cylinder having diameter 12 cm and height 15 cmis full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter6 cm, having a hemispherical shape on the top. Find the number of such cones which canbe filled with ice cream |
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Answer» Volume of ice cream = 3.142 x 6² x 15 = 1696.68Each child gets = 1696.68/10 = 169.668 cm³ Take radius of cone = r = radius of hemisphereHeight of cone is therefore = 4r Volume of hemisphere + volume of cone = 169.668 cm³ 2/3 x 3.142 x r³ + 1/3 x 3.142 x r² (4r) = 169.6682.09r³ + 4.19r³ = 169.6686.28r³ = 169.668 r³ = 27 r = 3 cm∴ Radius of cone = 3 Given: For right circular cylinder Diameter = 12 cm Radius(R1) = 12/2= 6 cm & height (h1) = 15 cm Volume of Cylindrical ice-cream container= πr1²h1= 22/7 × 6× 6× 15= 11880/7 cm³ Volume of Cylindrical ice-cream container=11880/7 cm³ For cone, Diameter = 6 cm Radius(r2) =6/2 = 3 cm & height (h2) = 12 cmRadius of hemisphere = radius of cone= 3 cm Volume of cone full of ice-cream= volume of cone + volume of hemisphere = ⅓ πr2²h2 + ⅔ πr2³= ⅓ π ( r2²h2 + 2r2³) = ⅓ × 22/7 (3²× 12 + 2× 3³) = ⅓ × 22/7 ( 9 ×12 + 2 × 27) = 22/21 ( 108 +54) = 22/21(162) = (22×54)/7 = 1188/7 cm³ Let n be the number of cones full of ice cream. Volume of Cylindrical ice-cream container =n × Volume of one cone full with ice cream 11880/7 = n × 1188/7 11880 = n × 1188 n = 11880/1188= 10 n = 10 Hence, the required Number of cones = 10 |
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