Question : A solid metallic sphere of radius 9 cm is melted and recasted into a wire of radius 2 cm. What is the length of the wire?
Option 1: 343 cm
Option 2: 152 cm
Option 3: 243 cm
Option 4: 184 cm
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Correct Answer: 243 cm
Solution : Given, A solid metallic sphere of radius 9 cm is melted and recast into a wire of radius 2 cm. We know, The volume of a sphere = $\frac43πr^3$, where $r$ is the radius And, the Volume of a wire = $πr^2l$, where $l$ is its length. ⇒ Volume of the sphere $=\frac43\pi ×9^3= 972\pi $ cm3 ⇒ Volume of the wire $=\pi(2)^2l=4\pi l$ cm3 The volume will remain the same $972 × \pi = 4 × \pi × l$ ⇒ $l=\frac{972}{4}$ ⇒ $l=243$ cm Hence, the correct answer is 243 cm.
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Question : A solid copper sphere of radius 6 cm is melted and redrawn into a wire, whose radius of cross-section is 8 cm. Find the length of the wire.
Option 1: 9 cm
Option 2: 2.25 cm
Option 3: 4.5 cm
Option 4: 6 cm
Question : A metallic solid sphere has a radius of 35 cm. If it is melted to form small spheres of radius 5 cm, then how many small spheres will be obtained?
Option 1: 343
Option 2: 289
Option 3: 429
Option 4: 369
Question : A sphere of radius 18 cm is melted and then a solid cylinder of base radius 4 cm is made from it. What is the height of the solid cylinder?
Option 1: 196 cm
Option 2: 486 cm
Option 3: 224 cm
Option 4: 384 cm
Question : A large solid cube is melted and cast into ' N ' small solid spheres, each of radius 3 cm, and ' N + 2 ' small solid cuboids, each of dimensions 4 cm × 4 cm × 6.5 cm. If the length of each side of the large solid cube is 12 cm, then find the value of 'N'. [Use $\left.\pi=\frac{22}{7}\right]$
Option 1: 8
Option 2: 5
Option 3: 7
Option 4: 6
Question : How many solid spheres of radius 3 cm can be formed by melting a bigger solid sphere of radius 24 cm?
Option 1: 512
Option 2: 128
Option 3: 64
Option 4: 256
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