iGCSE Mathematics (0580) - C5.4 Surface area and volume- Exam Style Questions Paper 1- New Syllabus
▶️ Answer/Explanation
The formula for computing the volume of a cube is simply the side length cubed ($V = s^3$). Substituting our value of $3\text{ cm}$ into this, we calculate $3 \times 3 \times 3 = 27\text{ cm}^3$.
✅ Answer: $27\text{ cm}^3$
✅ Answer: $27\text{ cm}^3$
▶️ Answer/Explanation
(a) A correct net must consist of $6$ rectangular faces layout out flat such that it can fold into a solid box: two $5 \times 2$ faces, two $5 \times 3$ faces, and two $3 \times 2$ faces, sharing matching edges properly.
(b) The formula for the volume of a standard cuboid is given by $\text{Volume} = \text{length} \times \text{width} \times \text{height}$. Substituting the given parameters: $5 \times 2 \times 3 = 30$. Since all dimensions are given in centimeters, the correct volume units are cubic centimeters ($\text{cm}^3$).
✅ Answer: (a) Fully correct 6-face layout net (b) $30\text{ cm}^3$
(b) The formula for the volume of a standard cuboid is given by $\text{Volume} = \text{length} \times \text{width} \times \text{height}$. Substituting the given parameters: $5 \times 2 \times 3 = 30$. Since all dimensions are given in centimeters, the correct volume units are cubic centimeters ($\text{cm}^3$).
✅ Answer: (a) Fully correct 6-face layout net (b) $30\text{ cm}^3$
▶️ Answer/Explanation
(a) The total surface area consists of 1 square base and 4 identical triangular faces.
$$\text{Area of the square base} = 5 \times 5 = 25\text{ cm}^2$$ $$\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 4 = 10\text{ cm}^2$$ $$\text{Area of all 4 triangles} = 4 \times 10 = 40\text{ cm}^2$$ $$\text{Total Surface Area} = 25 + 40 = 65\text{ cm}^2$$
(b) A square-based pyramid has 4 edges around the flat square base on the bottom, and 4 straight edges going up to the top peak (apex). This gives a total of $4 + 4 = 8$ edges.
Answers:
(a) 65 $\text{cm}^2$
(b) 8