11. A spherical ball of radius 3 cm is melted and recast into threes
balls. The radii of two of these balls are 1.5 cm and 2 cm. Find The radius of third ball
Answers
Answer:
The radius of spherical ball = 3 cm
Volume of spherical ball = 4/3πr^3
= 4/3π × 3 × 3 × 3
= 36π cm^3
The Volume of spherical ball = Total volume of three small spherical ball
∵ The radii of the ball are 1.5 cm and 2 cm
∴ Let the radius of third ball = r
∴ The Volume of spherical ball = Total volume of three small spherical balls
36π = 4/3π × (3/2)^3 + 4/3π × (2)^3 + 4/3 πr^3
36π = 4/3π × 27/8 + 4/3π × 8 + 4/3πr^3
36π = 4/3π( 27/8 + 8 + r^3)
(36π × 3)/4π = 27/8 + 8 + r^3
27 = (27 + 64)/8 + r^3
27 = 91/8 + r^3
27 – 91/8 = r^3
(216 – 91)/8 = r^3
125/8 = r^3
r = 3^√125/8
r = 5/2
The diameter of the third ball = 2r = 2 × 5/2
= 5 cm
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