  Question

# A container shaped like a right circular cylinder has a diameter (d) equal to 12 cm and height (h) equal to 15 cm is full of ice cream. The ice cream is to be filled into 10 equal cons having a hemispherical shape on the top. If the height of the cone is 4 times its radius, find the height of the cone.

Solution

## 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 cm Radius 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  Suggest corrections   