A spherical ball of radius 3 cm is melted and recast into three spherical balls
Answers
Explanation:
The radius of spherical ball = 3 cm
Volume of spherical ball = 4/3πr3
= 4/3π × 3 × 3 × 3
= 36π cm3
∵ 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
∴ Volume of spherical ball = Total volume of three small spherical balls
36π = 4/3π × (3/2)3 + 4/3π × (2)3 + 4/3 πr3
36π = 4/3π × 27/8 + 4/3π × 8 + 4/3πr3
36π = 4/3π(27/8 + 8 + r3)
(36π × 3)/4π = 27/8 + 8 + r3
27 = (27 + 64)/8 + r3
27 = 91/8 + r3
27 – 91/8 = r3
(216 – 91)/8 = r3
125/8 = r3
r = 5/2 cm
The diameter of the third ball = 2r = 2 × 5/2
= 5 cm
Answer:
Answer is 2.5cm
radius of sphere= 3cm
R1=1.5 cm
R2=2cm
R3=?
A/Q,
4/3πR^3=4/3πR1^3+4/3πR2^3+ volume of third sphere
R^3=R1^3+R2^3+R3^3
27=3.375+8+R3^3
27-11.37=R3^3
15.63=R3^3
R3=2.5 cm