Question

A container shaped like a right circular cylinder

having radius 6 cm and height 15 cm is full of

ice-cream. The ice-cream is to be filled into cones

of height 12 cm and radius 3 cm, having a

hemispherical shape on the top. Find the

number of such cones which can be filled with

ice-cream. ​

Answer 1

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Given:

For right circular cylinder

Diameter = 12 cm

Radius(R1) = 12/2= 6 cm & height = (h1) = 15 cm

Volume of Cylindrical ice-cream container= mr1?h13D 22/7 x 6x 6x 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 Radius of hemisphere = radius of

(h2) = 12 cm

cone= 3 cm

Volume of cone full of ice-cream= volume of cone + volume of hemisphere

= 3 Tr2?h2 + ?½ TIr2³= V3 1 ( r2²h2 + 2 r 2)

= V 3 x 22/7 (3?x 12 + 2x 33)

= V3 x 22/7 (9 ×12 + 2 x 27)

= 22/21 ( 108 +54)

= 22/21(162) =

= (22x54)/7 =

= 1188/7 cm3

Let n be the number of cones full of ice cream.

Volume of Cylindrical ice-cream container =n x Volume of one cone full with ice cream

11880/7 = n × 1188/7

11880 = n x 1188

n = 11880/1188= 10

n = 10

Hence, the required Number of

cones = 10

$\textbf{Hope\: it\: helps\: you\: ❤️ }$