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ICSE Class 10 Mathematics Question 19 of 21

Solved 2025 Specimen Paper ICSE Class 10 Mathematics — Question 14

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14
Question

Question 8(iii)

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 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=227)\Big(\text{use } \pi = \dfrac{22}{7}\Big)

Answer

(a) Given,

Radius of ball bearings = 7 mm

Volume of box = 2156 cm3 = 2156 × 103 mm3

Number of ball bearings that each box can have (N)

= Volume of boxVolume of each ball\dfrac{\text{Volume of box}}{\text{Volume of each ball}}

Substituting values we get :

N=2156×10343×227×73=2156×103883×72=2156×3×100088×49=64680004312=1500.N = \dfrac{2156 \times 10^3}{\dfrac{4}{3} \times \dfrac{22}{7} \times 7^3} \\[1em] = \dfrac{2156 \times 10^3}{\dfrac{88}{3} \times 7^2} \\[1em] = \dfrac{2156 \times 3 \times 1000}{88 \times 49} \\[1em] = \dfrac{6468000}{4312} \\[1em] = 1500.

Hence, maximum no. of ball bearings in a box = 1500.

(b) Mass of each box = No. of balls × Mass of each ball

= 1500 × 4 gm

= 6000 gm

= 60001000\dfrac{6000}{1000} = 6 kg.

Hence, mass of each box = 6 kg.