Find the Diameter of Each Sphere ?

Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is;

  1. 2cm
  2. 3 cm
  3. 4 cm
  4. 6 cm
Anurag Mishra Professor Asked on 8th October 2015 in Maths.
Add Comment
1 Answer(s)

Answer: (1) 2 cm

Explanation:-
Formula-
Volume of the cylinder V = Pai x r2 x h
Where, r = radius, h = height

Then, V = pai x 1 x 16
V = 16 pai
divide by 12,
Then, the volume of a small cylinder = 16 pai/12
= 4 pai /3

Formula-
Volume of sphere = 4 pai x (d/2)3
radius = diameter/2

Then, volume of sphere = 4 pai (d/2)3/3
4 pai/3 = 4 pai (d/2)3/3

1 = (d/2)3
Cube root on both side,
1 = d/2
by cross multiplication,
d = 2 cm

Then, the diameter of the sphere is 2 cm.

Hence, the answer is  (1) 2 cm.

Anurag Mishra Professor Answered on 11th October 2015.
Add Comment

Your Answer

By posting your answer, you agree to the privacy policy and terms of service.