**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 ****πr**^{2}**h**; 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 cm^{3}.

That being said, the volume of 504 cones would be **19.25/2 x 504 = 4851 cm**^{3}.

We also know that the volume of a sphere is **4/3 x πr**^{3}.

Melting the cones and recasting them into spheres, we have:

4/3 x 22/7 x r^{3} = 4851

r^{3} = (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!