A spherical ball of radius 3cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5cm and 2cm find the radius of the third ball.
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Given that radius of the spherical ball r = 3cm.
We know that volume of the sphere = 4/3pir^3
= 4/3 * 22/7 * (3)^3
= 4/3 * 22/7 * 27
= 4 * 22 * 9/7
= 792/7 cm^3.
= 113.1428
Given radii of the 1st sphere = 1.5cm
Volume of the 1st sphere = 4/3 pir^3
= 4/3 * 22/7 * (1.5)^3
= 4/3 * 22/7 * 3.375
= 14.1428.
Given radii of the 2nd sphere = 2cm.
the volume of the 2nd sphere = 4/3 pir^3
= 4/3 * 22/7 * (2)^3
= 33.5238.
Volume of the two small spheres = 14.1428 + 33.5238
= 47.6666.
Volume of the third sphere = 113.1428 - 47.6666
= 65.4762cm^3.
Let the radius of the third be r cm.
4/3pir^3 = 65.4762
4/3 * 22/7 * r^3 = 65.4762
r^3 = 65.4762 * 7/22 * 3/4
= 65.4762 * 21/88
= 1375.0002/88
= 15.62500
r = 2.5cm.
Therefore the radius of the third ball = 2.5cm.
Hope this helps!
We know that volume of the sphere = 4/3pir^3
= 4/3 * 22/7 * (3)^3
= 4/3 * 22/7 * 27
= 4 * 22 * 9/7
= 792/7 cm^3.
= 113.1428
Given radii of the 1st sphere = 1.5cm
Volume of the 1st sphere = 4/3 pir^3
= 4/3 * 22/7 * (1.5)^3
= 4/3 * 22/7 * 3.375
= 14.1428.
Given radii of the 2nd sphere = 2cm.
the volume of the 2nd sphere = 4/3 pir^3
= 4/3 * 22/7 * (2)^3
= 33.5238.
Volume of the two small spheres = 14.1428 + 33.5238
= 47.6666.
Volume of the third sphere = 113.1428 - 47.6666
= 65.4762cm^3.
Let the radius of the third be r cm.
4/3pir^3 = 65.4762
4/3 * 22/7 * r^3 = 65.4762
r^3 = 65.4762 * 7/22 * 3/4
= 65.4762 * 21/88
= 1375.0002/88
= 15.62500
r = 2.5cm.
Therefore the radius of the third ball = 2.5cm.
Hope this helps!
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