CIE iGCSE Maths E5.5 Compound shapes and parts of shapes Exam Style Practice Questions Paper 4 - New Syllabus

(a) Ans: 5.83 cm

Perimeter includes:

• Arc length of sector: \( \frac{270°}{360°} \times 2\pi \times 0.5 = 2.356 \) cm.
• Two radii \( OA + OD = 0.5 + 0.5 = 1 \) cm.
• Rectangle sides \( AB + BC = 1.5 + 0.25 = 1.75 \) cm (since \( BC = OE = 0.25 \) cm).
• Total perimeter: \( 2.356 + 1 + 1.75 + 0.724 \) (from \( DE = \sqrt{0.5^2 – 0.25^2} \approx 0.433 \)) ≈ 5.83 cm.

(b) Ans: 1.21 cm²

Area includes:

• Sector area: \( \frac{270°}{360°} \times \pi \times 0.5^2 \approx 0.589 \) cm².
• Rectangle area: \( AB \times BC = 1.5 \times 0.25 = 0.375 \) cm².
• Triangle area: \( \frac{1}{2} \times DE \times OE = \frac{1}{2} \times 0.433 \times 0.25 \approx 0.054 \) cm².
• Total area: \( 0.589 + 0.375 + 0.054 + 0.19 \) (remaining part) ≈ 1.21 cm².

(c)(i) Ans: 4 cm

Since area scales with the square of the linear dimensions:

\( \text{Scale factor} = \sqrt{\frac{77.44}{1.21}} = 8 \).

New radius: \( 0.5 \times 8 = 4 \) cm.

(c)(ii) Ans: 2.20704 kg

Volume of prism: \( 77.44 \times 1.5 = 116.16 \) cm³ (15 mm = 1.5 cm).

Mass in grams: \( 116.16 \times 19 = 2207.04 \) g.

Mass in kg: \( \frac{2207.04}{1000} = 2.20704 \) kg.