2. A cylindrical container having diameter16cm and height-40cmTsTui-of

1.	2. A cylindrical container having diameter16cm and height-40cmTsTui-of-ice.cream. The ice-cream is to be filled intocones of height 12 cm and diameter 4 chaving a hemispherical shape on the top.Find the number of such cones which canbe filled with the ice-cream.radiheiVolta
Answer» 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

2. A cylindrical container having diameter16cm and height-40cmTsTui-of-ice.cream. The ice-cream is to be filled intocones of height 12 cm and diameter 4 chaving a hemispherical shape on the top.Find the number of such cones which canbe filled with the ice-cream.radiheiVolta

Answer»

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