I/GCSE Mathematics Question Analysis Topic: Mathematics - Volume
Exam Question:
504 cones, each of diameter 3.5 cm and height 3 cm, are melted and recast into a metallic sphere. Find the diameter of the sphere . Use π = 22/7.
Answer:
For I/GCSE Mathematics, you should know:
We are give that r and h is 3.5/2 cm and 3 cm respectively.
The volume of a cone is 1/3 x πr2h; i.e. 1/3 x π (3.5/2)2 x 3 = 1/3 x 22/7 x 3.5/2 x 3.5/2 x 3 = 19.25/2 cm3.
That being said, the volume of 504 cones would be 19.25/2 x 504 = 4851 cm3.
We also know that the volume of a sphere is 4/3 x πr3.
Melting the cones and recasting them into spheres, we have:
4/3 x 22/7 x r3 = 4851
r3 = (4851 x 21)/88 = (441 x 21)/8
r = 21/2 = 10.5 cm
Hence, the diameter of the sphere is 2 x 10.5 = 21 cm.
Work hard for your I/GCSE Mathematics examination!
End of analysis. Great!