ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.5 in Chapter 17 - Mensuration

Question 20 Mensuration Exercise 17.5

How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm?



No matter how different the new shape is, when we change one solid shape into another, its volume stays the same. In reality, if we divide a large cube into numerous small spheres of lead, the total volume of the smaller spheres equals the volume of the original cube.

Edge of the cube, a = 44 cm

Volume of cube = a3

= 443

= 85184 cm3

Diameter of shot = 4 cm

So radius of shot, r = 4/2 = 2 cm

Volume of a shot = (4/3)π r3

= (4/3)×(22/7)×23

= 704/21 cm3

Number of lead shots made from cube = 85184÷(704/21)

= 85184×21/704

= 2541

Hence the number of shots made from cube is 2541.

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