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**I/GCSE** **Mathematics**** Question Analysis Topic: Mathematics - Volume**

**Exam Question:**

The volume of a sphere is increasing at the rate of 8cm3/s. Find the rate at which its surface area is increasing when the radius of the sphere is 12cm.

**Answer:**

For I/GCSE Mathematics, you should know:

__Definitions__**Volume of sphere V: (4/3)****πr**^{3}**Surface area of sphere S: 4****πr**^{2}

Now, the rate of volume and surface area is:

dV/dt = 4/3π x 3r^{2} x dr/dt

dS/dt = 4π x 2r x dr/dt

dV/dt = 8 cm^{3}/s

=> 4/3π x 3r^{2 }x dr/dt = *8*

=> dr/dt = (8 x 7)/(22 x 4 x 12^{2}) = *0.00441*

As such:

dS/dt = 4π x 2r x dr/dt = (4 x 22 x 2 x 12)/7 x 0.00441 = __65.33 cm__^{2}__/s__

Work hard for your I/GCSE Mathematics examination!

End of analysis. Great!