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I/GCSE Mathematics Question Analysis - Mathematics - Volume

I/GCSE Mathematics Question Analysis

· IGCSE Mathematics,mathematics,Volumes,Surface area

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)πr3
Surface area of sphere S: 4πr2

Now, the rate of volume and surface area is:

dV/dt = 4/3π x 3r2 x dr/dt
dS/dt = 4π x 2r x dr/dt
dV/dt = 8 cm3/s

=> 4/3π x 3r2 x dr/dt = 8
=> dr/dt = (8 x 7)/(22 x 4 x 122) = 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 cm2/s

Work hard for your I/GCSE Mathematics examination!

End of analysis. Great!

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