Rose Harrison and Clara Huizink Solutions for Exercise 23: Mixed practice

A supermarket sells $300\mathrm{ml}$ bottles of ketchup for $\pounds 1.30$ a bottle. In a special offer, if you buy two bottles you get one free. Is the total cost still in direct proportion to the number of bottles bought? Justify your answer.

The force needed to break a board varies inversely with the length of the board. It takes a force of $120$ Newtons to break a board $60 \mathrm{cm}$ long. Find the force needed to break a board $20 \mathrm{cm}$ long.

The number of tennis balls you can pack in a box varies inversely with the volume of the balls. Write down the variation function that expresses the relationship between the number of balls that can fit in a box and the radius of the balls.

A giraffe's weight varies directly with the cube of the animal's height. An adult giraffe is $5 \mathrm{m}$ tall and weighs $1.1$ metric tonnes. Find the weight of a $2 \mathrm{m}$ tall baby giraffe. 

During free-fall, the distance an object falls is directly proportional to the square of the time spent falling. An object falls $40.8 \mathrm{m}$ in $20 s$. Find how far it falls in $1$ minute.

The shutter speed of a camera varies inversely with the square of the aperture setting. When the aperture setting is $8$, the shutter speed is $125$. Find the shutter speed when the aperture setting is $4$.

The volume of a cylinder is given by the formula $V=\pi r^{2}h$, where $r$ is the radius of the base and $h$ is the height of the cylinder. If the cylinder has a fixed height, write down the variation function between $V$ and $r$. Hence, write down the proportionality constant in this case.

The volume of a cylinder is given by the formula $V=\pi r^{2}h$, where $r$ is the radius of the base and $h$ is the height of the cylinder. If the cylinder has a fixed radius, write down the variation function between $V$ and $h$. Hence, write down the proportionality constant in this case.