Circles, Area, Surface Area and Volume: math test solutions, Grade 7 – download the PDF

1 A circle / 3 pts

1. \(r = 20 \div 2 = 10\) cm. (1 pt)
2. \(C = 3.14 \times 20 = 62.8\) cm. (1 pt)
3. \(A = 3.14 \times 10^2 = 3.14 \times 100 = 314\) cm². (1 pt)

2 Triangles and quadrilaterals / 3 pts

1. \(A = \dfrac{1}{2} \times 15 \times 8 = 60\) cm². (1 pt)
2. \(A = 12 \times 7.5 = 90\) cm². (1 pt)
3. \(A = \dfrac{1}{2}(11 + 17) \times 6 = 14 \times 6 = 84\) cm². (1 pt)

3 A composite figure / 4 pts

1. \(12 \times 8 = 96\) in². (1 pt)
2. \(A = \dfrac{1}{2} \times 12 \times 5 = 30\) in². (2 pts: 1 for the formula, 1 for the result)
3. \(96 + 30 = 126\). The banner has an area of 126 in². (1 pt)

4 A triangular prism / 4 pts

1. Base area: \(\dfrac{1}{2} \times 5 \times 12 = 30\) cm². \(V = 30 \times 10 = 300\) cm³. (2 pts)
2. Two bases: \(2 \times 30 = 60\) cm². Rectangles: \((5 + 12 + 13) \times 10 = 300\) cm². \(SA = 60 + 300 = 360\) cm². (2 pts)

5 A square pyramid / 3 pts

Base: \(12 \times 12 = 144\) m². (1 pt)

One face: \(\dfrac{1}{2} \times 12 \times 10 = 60\) m², so four faces: \(240\) m². (1 pt)

\(SA = 144 + 240 = 384\) m². (1 pt)

6 A fish tank / 3 pts

1. \(50 \times 30 \times 40 = 60{,}000\) cm³. (1 pt)
2. \(50 \times 30 \times 30 = 45{,}000\) cm³. (1 pt)
3. \(45{,}000 \div 1{,}000 = 45\), so the tank holds 45 L of water. (1 pt)