Differentiation - rates of change¦KS5 maths¦Teachit - Free Printable

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1. The rate at which the area is increasing is 0.5π mm² s⁻¹.

2. The rate at which the radius is changing is 5/4π mm s⁻¹.

3. The rate of increase of the radius is 1/(180π) cm s⁻¹.

4. a. The rate of increase of its volume is 0.016π m³ s⁻¹.
b. The rate of increase of its surface area is 0.016π m² s⁻¹.

5. The depth h is changing at a rate of 1/67.2 m min⁻¹.

6. a. Since H = 3R, and for similar cones R = h/3, substituting into V = (1/3)πR²h gives V = (1/3)π(h/3)²h = (π/27)h³.
b. The rate of change of h is (9/(πh²)) cm s⁻¹.

7. The rate of change of power is -120e⁻³ᵗ watts per second.

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