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WAEC Further Mathematics 2023 Theory question 102

Theory question 102

Differentiation

The volume of a cube is increasing at the rate of 3½ cm3s−1. Find the rate of change of the side of the base when its length is 6 cm.

Show the model answer
Model answer

V = s³, so dV/dt = 3s² ds/dt.
3.5 = 3(36) ds/dt.
ds/dt = 3.5/108 = 7/216 ≈ 0.0324 cm s⁻¹.

Explanation

Connect the two rates with the chain rule.