three sprical metal ball of radii 6 cm,8cm and r cm are melted to form a solid sphere of radius 12cm . then,find the value of r
Answers
Given: metal ball of radii 6 cm,8cm and r cm, solid sphere of radius 12cm.
To prove: find the value of r=?
Solution:
- As we have given the three radius of the three given sphere, so lets write the volume of all the three.
- Volume of sphere is 4/3 π r³
Volume of sphere of radius 6 cm: 4/3 π (6)³
Volume of sphere of radius 8 cm: 4/3 π (8)³
Volume of sphere of radius x cm: 4/3 π (x)³
- Now volume of large sphere of radius 12 cm: 4/3 π (12)³
- As we have given that three spherical metal balls are melted to form a solid sphere, so:
Volume of all three spheres = volume of sphere of radius 12
4/3 π (6)³ + 4/3 π (8)³ + 4/3 π (x)³ = 4/3 π (12)³
- Solving this further, we get:
216 + 512 + x³ = 1728
x³ = 1000
x = 10 cm
Answer:
The radius of the third ball is 10 cm.
Given:
3 spherical balls or radius 6 cm, 8 cm and r cm.
They are melted to form a solid sphere of radius 12 cm.
To Find:
The value of r
Solution:
Find the volume of the sphere with radius 6 cm:
Volume = 4/3 πr³
Volume = 4/3 π(6)³
Volume = 288 π cm³
Find the volume of the sphere with radius 8 cm:
Volume = 4/3 πr³
Volume = 4/3 π(8)³
Volume = 2048/3 π cm³
Find the volume of the sphere with radius r cm:
Volume = 4/3 πr³
Find the volume of the sphere with radius 12 cm:
Volume = 4/3 πr³
Volume = 4/3 π(12)³
Volume = 2304 π cm³
Solve r:
288 π + 2048/3 π + 4/3 πr³ = 2304 π
4/3 πr³ = 400/3 π
r³ = 1000
r = 10
Answer: r is 10 cm