Q) A manufacturing company prepares spherical ball bearings, each of radius 7 mm and mass 4 gm. These ball bearings are packed into boxes. Each box can have a maximum of 2156 cm³ of ball bearings. Find the:
(a) maximum number of ball bearings that each box can have.
(b) mass of each box of ball bearings in kg.
(Use π = 22/7)

ICSE Specimen Question Paper – 2026

a) Step 1: We know that the volume of a sphere is given by, V = 4/3 pi r³
= 4/3 (22/7) (7/10)³
= 4/3 x 22 x 7 x 7/1000
= 4312/3000 cm³

Step 2: Now by unitary method, 4312/3 cm³ volume is taken by: 1 ball
Hence, 2156 cm³ will be taken by: 1 x 2156/(4312/3000)
= 3000/2
= 1500 ball bearings
Therefore each box can have maximum 1500 ball bearings.

b) Step 3: Mass of each box = Number of ball bearings x weight of 1 ball bearing
= 1500 x 4 gm
= 6000 gm
= 6 kg
Therefore mass of each box of ball bearings is 6 Kg.

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