A solid metallic sphere of radius x cm is melted and then drawn into 126 cones each of radius 3 5 cm...........

Quantitative Aptitude (CPO) Mensuration 3D

A solid metallic sphere of radius x cm is melted and then drawn into 126 cones each of radius 3.5 cm and height 3 cm. There is no

wastage of material in this process. What is the value of x?

This questions was previously asked in

SSC CPO 11th Dec 2019 Shift-1

10.5

3.5

Let’s break it down step by step:

- The volume of the original metallic sphere is (4/3)px³.

- After melting, the sphere is made into 126 cones, with each cone’s volume being (1/3)p(3.5)²×3.

- No wastage means the total volume is conserved: (4/3)px³ = 126 × (1/3)p(3.5)²×3.

- The (1/3)p and p cancel out easily.

- For the cone: (1/3)×p×(3.5)²×3 = p×12.25.

- Multiply by 126 cones: 126×12.25×p = 1543.5p.

- The sphere’s volume: (4/3)px³.

- Setting them equal: (4/3)px³ = 1543.5p ? x³ = (1543.5×3)/4 = 1157.625.

- Now, x = cube root of 1157.625 = 10.5.

Option analysis:

- Option 1: 10.5 Correct.

- Option 2: 7 (Too small)

- Option 3: 3.5 (Way too small)

- Option 4: 21 (Much too large)

So, the correct answer is option 1: 10.5.

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