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30.Acontaner shaped like a right, crcular cylinder having diameter 12 cn and height 15 em is fillof ice cream. The ice crean is to be filled into cones of height 12 cm and diameter 6 cm, havingberuispherical shape on the top. Fid the nimler of such cones wlych cay be filled with iceereainAns: 10 (NCERT Textbook Exercise 13.3 Q5) 2's 4x C |
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Answer» Given: For right circular cylinder Diameter = 12 cm Radius(R1) = 12/2= 6 cm & height (h1) = 15 cmVolume of Cylindrical ice-cream container= πr1²h1= 22/7 × 6× 6× 15= 11880/7 cm³Volume 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 cream11880/7 = n × 1188/711880 = n × 1188n = 11880/1188= 10n = 10Hence, the required Number of cones = 10 |
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