Question

a right circular cylindrical container of base radius 6 cm and height 15 cm is full of ice cream. the ice cream to be filled in cones of height 9 cm and base radius 3 cm, having a hemispherical cap. find the number of cones needed to empty the container

Answer 1

Answer:

12 cones

Step-by-step explanation:

Volume of Ice cream in the container = πr²h = 22/7 * (6)²(15) = 1697.14 cm³.

Volume of Ice cream cone = Volume of Hemisphere + volume of cone

                                            = 2/3πr³ + 1/3πr²h

                                            = 2/3 * 22/7 * (3)³ + 1/3 * 22/7* (3)² * 9

                                             = (3)²22/7 [2 + 3]

                                              = 5 * 9 * 22/7

                                              = 141.43 cm³

Thus number of cones required = 1697.14/141.43 = 12 cones.

Answer 2

12 cones are required to empty the container when Ice cream is within a right circular, cylindrical container with a base radius of 6 cm and a height of 15 cm.

Given that,

Ice cream is within a right circular, cylindrical container with a base radius of 6 cm and a height of 15 cm. Cones with a hemispherical top and a 9 cm height are to be filled with the ice cream.

We have to determine how many cones are required to empty the container.

We know that,

Volume of Ice cream in the cylindrical container = πr²h

= 3.14 × (6)²×(15)

= 1697.14 cm³.

Volume of Ice cream cone = Volume of Hemisphere + volume of cone

= $\frac{2}{3}$πr³ + $\frac{1}{3}$πr²h

= $\frac{2}{3}$ × 3.14 × (3)³ + $\frac{1}{3}$ × 3.14 × (3)² × 9

= (3)²×3.14× [2 + 3]

= 5 × 9 × 3.14

= 141.43 cm³

So, the number of cones required = $\frac{1697.14}{141.43}$ = 12 cones.

Therefore, 12 cones are required to empty the container when Ice cream is within a right circular, cylindrical container with a base radius of 6 cm and a height of 15 cm.

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