Question

The circumference of the base of a cylindrical vessel is 132 cm and its height is 28 cm. It is melted and recast into small hemispheres of diameter 14 cm. Calculate the number of small hemispheres formed.

Answer 1

ANSWER:

54 small hemispheres can be made

GIVEN:

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CYLINDER:

2π r = 132 cm => r = 132/2π

r = 132 × 7 ÷ 44

r = 3 × 7

r = 21 cm

h = 28 cm

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HEMISPHERE:

R = 14/2 = 7 cm

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TO FIND:

Number of hemispheres made(n).

FORMULAE:

Volume of cylinder = n × Volume of hemisphere

π r² h = n × 2/3 π R²

EXPLANATION:

r² h = 2/3 R² × n

n = 3 r² h ÷ 2R³

n = (3 × 21 × 21 × 28) ÷ (7 × 7 × 7 ×2)

n = (3 × 3 × 3 × 4)/ 2

n = 27 × 4/2

n = 27 × 2

n = 54

54 small hemispheres can be made.