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 maximum of 2156 cm ³ 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 (SQP)2025

Ans:

a) Step 1: According to question, number of spherical balls need to be kept into a box.

Here, we have radius of spherical ball as 7 mm

∴ radius of spherical ball, r  = 0.7 cm

Maximum capacity of the box is 2156 cm³

Step 2: We know the volume of a sphere, V_S = π r³

∴ V_S = (0.7)³

∴ V_S = (22 x 0.049) = cm³

Step 3: Now these balls need to be kept in a box of 2156 cm ³

By unitary method, we can say that:

∴ cm³  volume is for = 1 ball

∴ 2156 cm ³ volume will be for =

= balls

= balls

= balls

= 1500 balls

Therefore, the box can have maximum 1500 spherical balls.

(note: In step 2, we didn’t solve to avoid approximation error)

b) Mass of each box of ball bearings:

∵ mass of 1 spherical ball = 4 gm (given)

∴ mass of 1500 balls = 1500 x 4 = 6000 gm = 6 kg

Therefore, the mass of each box of ball bearings will be 6 kgs.

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