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

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Given

Dimensions of cylinderical container

• Radius, R = 6 cm
• Height, H = 15 cm

Dimensions of cone

• Radius of cone, r = 3 cm
• Height of cone, h = 9 cm
• Radius of hemispherical top, r = 3 cm

To find :-

Number of ice cream cones

Formula used

♡ Volume of cylinder =  π R² H

♡ Volume of cone = 1/3  π r² h

♡ Volume of hemisphere = 2/3  π r³

Solution:-

Let number of cones be 'n'

So, According to statement

Volume of cylinderical container = n × (Volume of cone + Volume of hemisphere)

π R² H = n × (1/3  π r² h + 2/3  π r³)

π R² H = n × 1/3 ×  π × r² × (h + 2r)

3 R² H = n × r² × (h + 2r)

3 × 6 × 6 × 15 = n × 3 × 3 × (9 + 6)

=> n = 12

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Answer 2

Answer:

n = 12 ...................