Question : How many solid spheres are made if a metallic cone of radius 12 cm and height 24 cm is melted into spheres of radius 2 cm each?
Option 1: 105
Option 2: 101
Option 3: 108
Option 4: 103
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Correct Answer: 108
Solution : Given: A metallic cone of radius 12 cm and height 24 cm is melted into spheres of radius 2 cm each We know, The volume of a cone = $\ \frac {1}{3}\pi r^2h$, where $r$ and $h$ are the radius and height of the cone respectively. So, the volume of the cone = $\frac{1}{3}×\pi×12^2×24$ cm3. Also the volume of a solid sphere = $\frac{4}{3}\pi R^3$, where $R$ is the radius. So, the volume of a solid sphere = $\ \frac {4}{3}×\pi×2^3$ cm3. Therefore, the required number of solid spheres = $\frac{\frac{1}{3}×\pi×12^2×24}{\frac{4}{3}×\pi×2^3}$ = $\frac{144×24}{4×8}$ = $108$ Hence, the correct answer is 108.
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Question : 24 equal solid hemispheres are melted to form a right circular cylinder of radius 12 cm and height 24 cm. Find the radius of each solid hemisphere.
Option 1: 4 cm
Option 2: 8 cm
Option 3: 6 cm
Option 4: 3 cm
Question : A metallic sphere of radius 21 cm is melted and then recast into smaller cones, each with a 7 cm radius and a height of 3 cm. Find the number of cones obtained.
Option 1: 225
Option 2: 325
Option 3: 522
Option 4: 252
Question : A metallic sphere of radius 10 cm is melted and then recast into small cones each of radius 3.5 cm and height 3 cm. The number of cones thus formed is:
Option 1: 140
Option 2: 132
Option 3: 112
Option 4: 126
Question : How many solid spherical balls of radius 6 cm can be made by melting a solid hemisphere of radius 12 cm?
Option 1: 4
Option 2: 2
Option 3: 10
Option 4: 8
Question : A solid cuboid is melted to form several cubes. If the length, breadth and height of a cuboid are 20 cm, 16 cm and 8 cm and the edge of each cube is 4 cm, then the number of cubes is:
Option 1: 50
Option 2: 44
Option 3: 40
Option 4: 48
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