Question : The number of balls, each one is 4 cm in the diameter that can be made from a solid metallic sphere of diameter 32 cm is:
Option 1: 256
Option 2: 64
Option 3: 512
Option 4: 1024
Correct Answer: 512
Solution : Let $n$ be the number of balls made. Given, The radius of new spherical balls (r) = 2 cm The radius of the bigger ball (R) = 16 cm Volume of bigger ball = n(Volume of smaller balls) ⇒ $\frac43\pi R^3=n(\frac43\pi r^3)$ ⇒ $16\times16\times16=n\times2\times2\times2$ $\therefore n = 512$ Hence, the correct answer is 512.
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Question : A solid sphere made of wax of radius 12 cm is melted and cast into solid hemispheres of radius 4 cm each. Find the number of such solid hemispheres.
Option 1: 54
Option 2: 27
Option 3: 14
Option 4: 28
Question : How many metallic spheres, each of diameter 6 cm can be melted to mould into a solid cylinder of diameter 8 cm and height of 18 cm?
Option 1: 6
Option 2: 12
Option 3: 8
Option 4: 10
Question : Two metallic balls P and Q are such that the diameter of P is four times the diameter of Q. What is the ratio between the volumes of P and Q?
Option 1: 32 : 1
Option 2: 16 : 1
Option 3: 8 : 1
Option 4: 64 : 1
Question : A solid metallic sphere of radius 8.4 cm is melted and recast into a right circular cylinder of radius 12 cm. What is the height of the cylinder? (Your answer should be correct to one decimal place.)
Option 1: 6.5 cm
Option 2: 5.5 cm
Option 3: 7.0 cm
Option 4: 6.0 cm
Question : A solid metallic sphere of radius 6.3 cm is melted and recast into a right circular cone of height 25.2 cm. What is the ratio of the diameter of the base to the height of the cone?
Option 1: 2 : 1
Option 2: 3 : 2
Option 3: 1 : 2
Option 4: 2 : 3
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