The diagram shows a circular table top of radius \(0.6\) m. The top is to be covered with glass costing \(\$85\) for each square metre. Calculate the cost o...
Question 1 Report
The diagram shows a circular table top of radius \(0.6\) m. The top is to be covered with glass costing \(\$85\) for each square metre.
Calculate the cost of the glass, giving your answer correct to the nearest cent.
Answer Details
The glass covers the circular top, so the amount needed is the area of a circle, \( A = \pi r^{2} \), with the radius given directly as \( 0.6 \) m.
\[ A = \pi \times 0.6^{2} = \pi \times 0.36 = 1.130973\ldots \text{ m}^2 \] [M1]Each square metre of glass costs \( \$85 \), so the cost is the area multiplied by the price per square metre:
\[ 1.130973\ldots \times 85 = 96.1327\ldots \] [M1]Correct to the nearest cent, the glass costs \( \$96.13 \) [A1].
Square the radius before multiplying by \( \pi \), since \( \pi \times 0.6^{2} \) is not the same as \( (\pi \times 0.6)^{2} \). The units also work in your favour as a check: an area in square metres multiplied by dollars for each square metre leaves dollars. Keep the unrounded area on the calculator, because rounding it to \( 1.13 \) first would give \( \$96.05 \) and lose the accuracy mark.
Download The App On Google Playstore
Everything you need to excel in your exams
