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?
Answer & explanation
Correct answer: option 1
We know that,
The volume of sphere = \(\frac{4}{3}\)πR3
Volume of cone = \(\frac{1}{3}\)πr2h
We have,
Total number of cones = 126
Radius and Height of cone = 3.5 cm and 3 cm respectively.
According to the question
\(\frac{4}{3}\)πx3 = 126 × \(\frac{1}{3}\) × πr2h
= x3 = \(\frac{126}{4}\) × 3.5 × 3.5 × 3
= x3 = 3 × 3 × 3.5 × 3.5 × 3.5 × 3 = 10.5 cm