Ratio, scale and sharing: Practice Questions

A map has a scale of \(1 : 50\,000\).
The distance between two towns on the map is \(8\text{ cm}\).
Calculate the actual distance between the two towns in kilometres.

\(y\) is inversely proportional to the square of \(x\).
When \(x = 3\), \(y = 4\).
Find the value of \(y\) when \(x = 2\).

Solid \(A\) and Solid \(B\) are mathematically similar. The ratio of the surface area of \(A\) to the surface area of \(B\) is \(9 : 25\).
If the volume of Solid \(A\) is \(54\text{ cm}^3\), calculate the volume of Solid \(B\).

Express \(75\text{ cm}\) as a fraction of \(2\text{ m}\) in its simplest form.

A metal block has a density of \(8\text{ g/cm}^3\) and a mass of \(1.2\text{ kg}\).
Calculate the volume of the block.

A contractor needs to mix concrete using cement, sand, and gravel in the ratio \(2 : 3 : 5\) by mass.
(a) The contractor has \(45\text{ kg}\) of sand. Calculate the mass of cement and the mass of gravel he needs to use all of the sand.
(b) Concrete has a density of \(2400\text{ kg/m}^3\). Calculate the volume of concrete produced if the total mass of the mixture is \(600\text{ kg}\).
(c) If the price of cement increases by \(15\%\), and cement originally cost \(\pounds 8.40\) per \(25\text{ kg}\) bag, calculate the new cost of one bag.