iGCSE Mathematics (0580) - C5.4 Surface area and volume- Exam Style Questions Paper 3- New Syllabus
▶️ Answer/Explanation
(a)
A cube has 6 identical square faces. Find the area of one face:
$121.5 \div 6 = 20.25$ cm$^2$
The side length is the square root of the face area: $\sqrt{20.25} = 4.5$ cm
✅ Answer: $4.5$ cm
(b)
(i) Use the formula for the area of a trapezium: Area = $\frac{1}{2}(a+b)h$
$106.25 = \frac{1}{2}(10 + 15) \times h$
$106.25 = 12.5 \times h \implies h = \frac{106.25}{12.5} = 8.5$ cm
✅ Answer: $8.5$ cm
(ii) To convert cm$^2$ to m$^2$, divide by $10,000$ (since $1 \text{ m} = 100 \text{ cm}$, $1 \text{ m}^2 = 10,000 \text{ cm}^2$):
$106.25 \div 10000 = 0.010625$ m$^2$
✅ Answer: $0.010625$ m$^2$
▶️ Answer/Explanation
First, we calculate the volume of the cylinder using the formula $V = \pi r^2 h$.
$V = \pi \times 5^2 \times 12 = 300\pi \approx 942.477\text{ cm}^3$
Since the cube shares the same volume, we set the cube’s volume formula $x^3$ equal to this value.
$x^3 = 942.477$
$x = \sqrt[3]{942.477} \approx 9.80$
✅ Answer: 9.80