The external diameter of a hollow metal sphere is 14 cm and its thickness is 2 cm find the radius of a solid sphere containing same amount of material as hollow sphere.
Answers
•external diameter = 14 cm
•Radius of a solid sphere is
6.073 cm
•external radius = R = 7 cm
•internal radius = external radius -
thickness
•internal radius = r = 5
•Now , Volume of material in hollow
sphere = 4π( R³-r³)/3
= 4π(7³-5³)/3
= 4π(349-125)/3
= 4π(224)/3
•Now let the required sphere has
radius = R'
•Volume of required sphere =
4π(R'³)/3
•According to question
•Volume of required sphere = •Volume of material in hollow
sphere
• 4π(R'³)/3 = 4π(224)/3
• R'³ = 224
• R' = 6.073 cm
Answer:
6 cm
Step-by-step explanation:
External diameter = 14 cm
⇒ External radius = 14 ÷ 2 = 7 cm
Find the internal radius:
Internal radius = 7 - 2 = 5 cm
Find the volume of the sphere with radius 7 cm:
Volume = 4/3 πr³
Volume = 4/3 π(7)³
Volume = 1372π/3 cm³
Find the volume of the sphere with radius 5 cm:
Volume = 4/3 πr³
Volume = 4/3 π(5)³
Volume = 500π/3 cm³
Find the volume of the material used:
Volume of material = 1372π/3 - 500π/3
Volume of material =872π/3 cm³
Find the radius of a sphere with the same amount of material:
Volume = 4/3 πr³
872π/3 = 4/3 πr³
r³ = 872π/3 ÷ 4π/3
r³ = 218
r = 6 cm
Answer: 6 cm