A $60 \pi \mathrm{cm}$ B $80 \pi \mathrm{cm}$ Extended-response questions 1 An office receives five new desks with a bench shape made up of a rectangle and quarter-circle as shown. The edge of the bench is lined with a rubber strip at a cost of $\$ 2.50$ per metre. a Find the length, in centimetres, of the rubber edging strip for one desk correct to two decimal places. b By converting your answer in part a to metres, find the total cost of the rubber strip for the five desks. Round to the nearest dollar. The manufacturer claims that the desktop area space is more than $1.5 \mathrm{~m}^{2}$. c Find the area of the desktop in $\mathrm{cm}^{2}$ correct to two decimal places. d Convert your answer to $\mathrm{m}^{2}$ and determine whether or not the manufacturer's claim is correct.

Step 1 ：Let the length of the rectangle be $l$ and the width be $w$. The radius of the quarter-circle is also $w$.

Step 2 ：The length of the rubber edging strip for one desk is the sum of the rectangle's perimeter and the quarter-circle's circumference. So, the total length is $l + 2w + \frac{1}{4}(2\pi w) = l + 2w + \frac{1}{2}\pi w$.

Step 3 ：Substitute the given values: $l = 60\pi$ and $w = 80\pi$. Then, the length of the rubber edging strip is $60\pi + 2(80\pi) + \frac{1}{2}\pi(80\pi) \approx 320.42$ cm.

Step 4 ：Convert the length to meters: $320.42 \text{ cm} = 3.2042 \text{ m}$. The total cost of the rubber strip for the five desks is $5(3.2042) \times 2.50 \approx \boxed{40}$ dollars.

Step 5 ：The area of the rectangle is $lw = (60\pi)(80\pi) = 4800\pi^2 \text{ cm}^2$. The area of the quarter-circle is $\frac{1}{4}\pi w^2 = \frac{1}{4}\pi(80\pi)^2 = 1600\pi^3 \text{ cm}^2$. The total area of the desktop is $4800\pi^2 + 1600\pi^3 \approx 15053.42 \text{ cm}^2$.

Step 6 ：Convert the area to square meters: $15053.42 \text{ cm}^2 = 1.505342 \text{ m}^2$. Since $1.505342 > 1.5$, the manufacturer's claim is \boxed{correct}.