O-LevelAdditional MathematicsDifferentiation and integration4037/12 · May/June 2020 · Q24 Marks
The volume, V, of a sphere of radius r is given by V = 4/3 πr². The radius, r cm, of a sphere is increasing at the rate of 0.5 cms⁻¹. Find, in terms of π, the rate of change of the volume of the sphere when r = 0.25.
- The volume, V, of a sphere of radius r is given by V = 4/3 πr². The radius, r cm, of a sphere is increasing at the rate of 0.5 cms⁻¹. Find, in terms of π, the rate of change of the volume of the sphere when r = 0.25.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [1] dr/dt = 0.5
- [1] dV/dr = 4πr²
- [1] For attempt to use a correct form of the chain rule
- [1] When r = 1/4, dV/dt = 0.125π
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