A solid sphere has a radius 21 cm. It is melted to form a cube. 20% material is wasted in this process. The cube is melted to form hemisphere. In this process 20% material is wasted. The hemisphere is melted to form two spheres of equal radius. 20% material was also wasted in this process. What is the radius (in cm) of each new sphere?
A) 4.2 (23) B) 2.1 23 C) 2.1 43 D) 4.2 43
Answers
Given: A solid sphere has a radius 21 cm. It is melted to form a cube. 20% material is wasted in this process. The cube is melted to form hemisphere. In this process 20% material is wasted. The hemisphere is melted to form two spheres of equal radius. 20% material was also wasted in this process.
To find: What is the radius (in cm) of each new sphere?
Solution:
- Now we have given that the material is wasted 20% three times, so according to question,, the equation is:
4/3 x π x 21³ x (1 – 20/100)³ = 2 x 4/3 x πr³
- Here r is the radius of two new spheres formed.
- Solving the equation, we get:
21³ x (1 – 20/100)³ = 2 x πr³
21³ x (4/5)³ = 2 x r³
21³ x (4/5)² x 2/5 = r³
r³ = { (2 x 21) / 5}³ x 4
r = (42/5) x ∛4
r = 8.4 ∛4 cm
Answer:
So the radius (in cm) of each new sphere is 8.4 ∛4 cm .