2016 Paper 1 Q7

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Air is pumped into a spherical exercise ball at the rate of 250 cm³ per second.

Find the rate at which the radius is increasing when the radius of the ball is 20 cm.

Give your answer in the form $\frac{a}{b\pi}$ and then enter $\left(a,b\right)$ into the computer.

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Find the rate at which the surface area of the ball is increasing when the radius of the ball is 20 cm.

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The inflated ball is kicked into the air from a point O on the ground. Taking O as the origin, $\left(x,\ f\left(x\right)\right)$ approximately describes the path followed by the ball in the air, where

$f\left(x\right)=-x^2+10x$

and both $x$ and $f\left(x\right)$ are measured in metres.

Find the values of $x$ when the ball in on the ground.

Give your answer as a point with the smallest value first

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Find the average height of the ball above the ground, during the interval from when it is kicked until it hits the ground again.