February 22, 2023
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!