A certain number of identical spheres are formed by melting a large sphere of radius 28 cm. What is the number of small spheres formed if the surface area of each small sphere is 2464 cm ? [Use π = $\frac{22}{7}$]
Answer & explanation
Correct answer: option 1
We know that,
We know that the volume of the sphere = \(\frac{4}{3}\)πr3
According to the question,
4πr2 = 2464
r2 = 2464 × \(\frac{7}{88}\)
r2 = 196
r = 14
Volume of each smaller sphere = (\(\frac{4}{3}\)π143) cm3
Let number of sphere can be made = x
According to the concept,
x(\(\frac{4}{3}\) × π × 143) = (\(\frac{4}{3}\) × π × 283)
= x × 143 = 23 × 143
= x = 8