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
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Correct Answer: 252
Solution : Let the number of cones made be $n$. In this case, the metallic sphere is melted and then cast into smaller cones. So, Volume of Sphere $= n\times$ Volume of cone ⇒ $\frac{4}{3}\pi r{_s}^3=n\times\frac{1}{3}\pi r{_c}^2h$ where $r_s$ is the radius of the sphere, $r_c$ is the radius of the cone, and $h$ is the height of the cone. ⇒ $4\times r{_s}^3=n\times r{_c}^2h$ ⇒ $4\times (21)^3=n\times (7)^2\times 3$ ⇒ $n=\frac{4\times 21\times 21\times 21}{7\times 7\times 3}$ ⇒ $n=4\times3\times 21$ ⇒ $n=252$ Hence, the correct answer is 252.
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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 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
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 : The radius and slant height of a cone are in the ratio 5 : 7. If its curved surface area is 1347.5 cm2, find its radius. $\mathrm{(Use ~\pi =\frac{22}{7})}$
Option 1: 15 cm
Option 2: 25.5 cm
Option 3: 17.5 cm
Option 4: 21 cm
Question : What is the height of a cylinder that has the same volume and radius as a sphere of diameter 12 cm?
Option 1: 7 cm
Option 2: 10 cm
Option 3: 9 cm
Option 4: 8 cm
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