Measurement: Surface Area, Volume & Scaling (Grade 10) — Worksheet & Memo

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Grade 10 · Measurement

Measurement: Surface Area, Volume & Scaling (Grade 10)

MEMORANDUM

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Mark

/ 48

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
A cube has a volume of 216 cm³. Determine the length of one edge, and hence the total surface area of the cube.
(4)
edge = ∛216 = 6 cm (2)
A cube has 6 square faces, so SA = 6 × 6² (1)
= 216 cm² (1)✓✓✓✓ (4)
2
The diagram below shows a cylinder. Calculate its volume. (π ≈ 3,14)
(3)
3,14 × 25 × 12 = 942 cm³✓✓✓ (3)
3
The diagram below shows a cone. Calculate its volume. (π ≈ 3,14)
(3)
⅓ × 3,14 × 9 × 4 = 37,68 cm³✓✓✓ (3)
4
Calculate the volume of the sphere in the diagram below. (π ≈ 3,14)
(3)
4/3 × 3,14 × 27 = 113,04 cm³✓✓✓ (3)
5
Calculate the surface area of the sphere in the diagram below. (π ≈ 3,14)
(3)
4 × 3,14 × 36 = 452,16 cm²✓✓✓ (3)
6
The diagram below shows a pyramid. Calculate its volume.
(3)
⅓ × 30 × 9 = 90 cm³✓✓✓ (3)
7
The diagram below shows a right pyramid with a square base of side 18 cm and a perpendicular height of 12 cm. Calculate the slant height ℓ and the total surface area of the pyramid.
(5)
Half the base edge = 9 cm; ℓ² = 12² + 9² = 225, so ℓ = 15 cm (2)
Base = 18² = 324 cm² (1); four faces = 4 × 1/2 × 18 × 15 = 540 cm² (1)
TSA = 324 + 540 = 864 cm² (1)✓✓✓✓✓ (5)
8
The diagram below shows a right pyramid whose base is an equilateral triangle with sides of 8 cm. The slant height of each sloping face is 10 cm. Calculate the total surface area of the pyramid.
(4)
Height of the base triangle = √(8² − 4²) = √48 ≈ 6,93 cm (1)
Base area = 1/2 × 8 × √48 ≈ 27,71 cm² (1)
Three faces = 3 × 1/2 × 8 × 10 = 120 cm² (1)
TSA ≈ 147,71 cm² (1)✓✓✓✓ (4)
9
A solid's dimensions are all doubled. What happens to its volume?
(2)
It becomes 8 times bigger (2³).✓✓ (2)
10
A solid's dimensions are all tripled. What happens to its surface area?
(2)
It becomes 9 times bigger (3²).✓✓ (2)
11
The diagram below shows a triangular prism. Calculate its volume.
(3)
½ × 6 × 4 = 12 cm²; 12 × 10 = 120 cm³✓✓✓ (3)
12
Calculate the volume of the cylinder in the diagram below. (π ≈ 3,14)
(3)
3,14 × 16 × 8 = 401,92 cm³✓✓✓ (3)
13
The solid in the diagram below is a cylinder of radius 4 cm and height 10 cm with a cone of height 3 cm on top. Calculate the volume and the total surface area of the solid, correct to TWO decimal places.
(6)
V = π(4)²(10) + 1/3π(4)²(3) = 160π + 16π = 176π ≈ 552,92 cm³ (2)
Slant height of the cone: ℓ = √(3² + 4²) = 5 cm (1)
TSA = base + curved wall + curved cone = π(4)² + 2π(4)(10) + π(4)(5) (1)
= 16π + 80π + 20π = 116π ≈ 364,42 cm² (1)
The circle where the cone meets the cylinder is sealed inside and is not counted (1)✓✓✓✓✓✓ (6)
14
A cube with edges of 3 cm is glued to the centre of the top of a cube with edges of 6 cm, as in the diagram below. Calculate the total surface area of the solid.
(3)
Large cube: 6 × 6² = 216 cm²; small cube: 6 × 3² = 54 cm² (1)
The joined 3 cm by 3 cm square is hidden on BOTH cubes: subtract 2 × 9 = 18 cm² (1)
TSA = 216 + 54 − 18 = 252 cm² (1)✓✓✓ (3)
15
Which two solids have a ⅓ in their volume formula?
(1)
The cone and the pyramid✓ (1)

TOTAL: 48 marks