If a solid sphere of radius 10 cm is moulded into 8 spherical solid ba

1.	If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq. cm) is :A. 100π B. 75π C. 60π D. 50π
Answer» Option : (A) Volume of sphere = \(\frac{4}{3}\)πr³ Given, solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius ⇒ \(\frac{4}{3}\)π × 10³ = 8 × \(\frac{4}{3}\)π × r³ ⇒ r= \(\frac{10}{2}\)= 5cm Surface area of a sphere = 4πr² Thus, the surface area of each sphere = 4 × π × 5² = 100π

If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq. cm) is :A. 100π B. 75π C. 60π D. 50π

Answer»

Option : (A)

Volume of sphere = \(\frac{4}{3}\)πr³

Given,

solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius

⇒ \(\frac{4}{3}\)π × 10³ = 8 × \(\frac{4}{3}\)π × r³

⇒ r= \(\frac{10}{2}\)= 5cm

Surface area of a sphere = 4πr²

Thus,

the surface area of each sphere = 4 × π × 5²

= 100π