Solids, plans and elevations

(a) $9$

1. The two triangular faces each have 3 edges: 2 $\times$ 3 = 6.
2. Three more edges join corresponding vertices, so 6 + 3 = 9.

• B1 Correct answer: $9$

(a) 5

1. 2 triangles and 3 rectangles make 5 faces.

• B1 Correct answer: 5 faces.

(b) 9

1. 3 edges on each triangle and 3 joining them: 9.

• B1 Correct answer: 9 edges.

(c) 6

1. 3 corners on each triangular end: 6.

• B1 Correct answer: 6 vertices.

(a) $24\text{ cm}^3$

1. The plan gives length 4 cm and depth 3 cm; the front elevation gives height 2 cm.
2. $$4 \times 3 \times 2 = 24$$

• M1 Identifying the three dimensions 4, 3 and 2 and multiplying them.
• A1 $24\text{ cm}^3$.

(b) $52\text{ cm}^2$

1. Three different faces: $4 \times 3 = 12$, $4 \times 2 = 8$, $3 \times 2 = 6$.
2. Each appears twice.
   $$2(12 + 8 + 6) = 52$$

• P1 Finding the areas of the three different faces.
• P1 Doubling the sum of the three areas.
• A1 $52\text{ cm}^2$.

(a) $12$ unit squares

1. $$3+5+4$$
2. In each column the front elevation shows the taller of the front and back stacks.
3. The visible column heights are max(2,3) = 3, max(1,5) = 5 and max(4,2) = 4.
4. Its area is 3 + 5 + 4 = 12 unit squares.

• P1 Establishing $3+5+4$ or an equivalent valid method.
• A1 Correct answer: $12$ unit squares

(a) $9$

1. For each column use the taller of the front and back stacks.
   $$2+4+3$$
2. Therefore $9$.

• M1 For each column use the taller of the front and back stacks.
• A1 Correct answer: $9$

(b) $13$

1. Add the heights of all six stacks.
   $$2+1+3+2+4+1$$
2. Therefore $13$.

• M1 Add the heights of all six stacks.
• A1 Correct answer: $13$

(a) A circle

1. A circle.

• B1 Correct answer: A circle

(b) A rectangle 6 cm wide and 10 cm tall.

1. A rectangle 6 cm wide and 10 cm tall.

• C1 Correct conclusion with supporting reasoning: A rectangle 6 cm wide and 10 cm tall.

(c) $60$ cm²

1. Multiply the diameter by the height.
   $$6\times 10$$
2. Therefore $60$ cm².

• M1 Multiply the diameter by the height.
• A1 Correct answer: $60$ cm²

(a) $8$

1. Therefore $8$.

• B1 Correct answer: $8$

(b) A 6 cm square with both diagonals drawn; they meet at the centre, directly below the apex.

1. A 6 cm square with both diagonals drawn; they meet at the centre, directly below the apex.

• C1 Correct conclusion with supporting reasoning: A 6 cm square with both diagonals drawn; they meet at the centre, directly below the apex.

(c) $12$ cm²

1. Use base 6 cm and height 4 cm.
   $$6\times 4/2$$
2. Therefore $12$ cm².

• M1 Use base 6 cm and height 4 cm.
• A1 Correct answer: $12$ cm²

(a) A rectangle

1. A rectangle.

• B1 Correct answer: A rectangle

(b) $9000$ cm²

1. Convert both visible lengths to centimetres.
   $$1.2\times 100=120$$
2. Multiply the front width by the height, not the depth.
   $$120\times 75$$
3. Therefore $9000$ cm².

• P1 Convert both visible lengths to centimetres.
• P1 Multiply the front width by the height, not the depth.
• A1 Correct answer: $9000$ cm²

(c) $360$ litres

1. Multiply the three centimetre dimensions, then convert volume units.
   $$120\times 75\times 40/1000$$
2. Therefore $360$ litres.

• P1 Multiply the three centimetre dimensions, then convert volume units.
• A1 Correct answer: $360$ litres