The plan of a classroom is drawn to a scale of \(1:50\). On the plan the classroom is a rectangle measuring \(16\) cm by \(12\) cm. (a) Calculate the actual...
Question 1 Report
The plan of a classroom is drawn to a scale of \(1:50\). On the plan the classroom is a rectangle measuring \(16\) cm by \(12\) cm.
(a) Calculate the actual length and the actual width of the classroom, in metres. [2]
(b) Calculate the actual area of the floor, in square metres. [1]
(c) Floor tiles cost \(\$23.50\) for each square metre. Calculate the cost of tiling the floor. [1]
Answer Details
The scale \(1:50\) is unit free, so a plan length in centimetres multiplied by \(50\) gives the real length in centimetres. The later parts then use the real lengths to find an area and a cost.
(a) Length:
\[ 16 \times 50 = 800 \text{ cm} \] [M1] \[ 800 \div 100 = 8 \text{ m} \]Width:
\[ 12 \times 50 = 600 \text{ cm} = 6 \text{ m} \]So the classroom is \(8\) m by \(6\) m. [A1]
(b) The floor is a rectangle:
\[ 8 \times 6 = 48 \text{ m}^2 \] [B1](c) Each square metre costs \( \$23.50 \), so the total cost is
\[ 48 \times 23.50 = \$1128 \] [B1]Two checks are useful. The area could also be found from the plan area \(16 \times 12 = 192\) cm\(^2\) multiplied by \(50^{2}\), giving \(480\,000\) cm\(^2\), which is \(48\) m\(^2\) since \(1\) m\(^2 = 10\,000\) cm\(^2\). And a cost in dollars should be written with the dollar sign and, if it had not come out exact, to two decimal places.
Download The App On Google Playstore
Everything you need to excel in your exams
