O-LevelAdditional MathematicsDifferentiation and integration4037/22 · May/June 2010 · Q34 Marks
The volume V cm³ of a spherical ball of radius r cm is given by V = (4/3)πr³. Given that the radius is increasing at a constant rate of 1/π cm s⁻¹, find the rate at which the volume is increasing when V = 288π.
- (a)The volume V cm³ of a spherical ball of radius r cm is given by V = (4/3)πr³. Given that the radius is increasing at a constant rate of 1/π cm s⁻¹, find the rate at which the volume is increasing when V = 288π.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.
- B1 for dV/dr = 4πr²
- B1 for r=6
- M1 for Uses dV/dt = dV/dr × dr/dt
- A1 for 144
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