(a) Here is a shape made from a rectangle and a semicircle.
Diagram NOT accurately drawn
The length of the rectangle is 7.1 cm. The radius of the semicircle is 2.7 cm. Work out the area of the shape. Give your answer correct to 3 significant figures. (4)
(b) Here is another shape made from a rectangle and a semicircle.
Diagram NOT accurately drawn
The length of the rectangle is \(L\) cm. The radius of the semicircle is \(r\) cm. The perimeter, \(P\) cm, of the shape is given by the formula \[P = \pi r + 2L + 2r\] Make \(r\) the subject of the formula \(P = \pi r + 2L + 2r\). (3)
Mark scheme (a)
Scheme
Marks
Splits shape into rectangle & semicircle
M1
\(\dfrac{\pi \times 2.7^2}{2}\) or value rounding to 11.4 or 11.5
M1
2 × 2.7 × 7.1 or 38.34
M1
49.8
A1
(4)
Notes
M1: May be implied by working
M1: \(\pi\) → 11.451105…
3.14 → 11.4453
3.142 → 11.45259
Also award for equivalent multiple of \(\pi\) eg \(3.645\pi\), \(\dfrac{729\pi}{200}\)
M1: Also accept 38.3
A1: for 49.8 or for answer rounding to 49.78 or 49.79
Mark scheme (b)
Scheme
Marks
\(P - 2L = \pi r + 2r\) oe
M1
\(P - 2L = (\pi + 2)r\) oe
M1
\(\dfrac{P - 2L}{\pi + 2}\) oe
A1
(3)
(Total 7 marks)
Notes
M1: for rearranging with both \(r\) terms on one side
M1: for factorising a correct expression (does not depend on a correct rearrangement)
