Surface Area & Volume of 3-D Objects (Grade 9) — Worksheet & Memo

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Grade 9 · Surface Area and Volume of 3D Objects

Surface Area & Volume of 3-D Objects (Grade 9)

MEMORANDUM

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/ 31

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 512 cm³. Determine the length of one edge, and hence the total surface area of the cube.
(4)
edge = ∛512 = 8 cm (2)
A cube has 6 square faces, so SA = 6 × 8² (1)
= 384 cm² (1)✓✓✓✓ (4)
2
Volume of a box 6 cm × 4 cm × 3 cm.
(2)
72 cm³✓✓ (2)
3
Surface area of a box 6 cm × 4 cm × 3 cm.
(3)
2(24 + 18 + 12) = 108 cm²✓✓✓ (3)
4
Volume of a cube with side 5 cm.
(1)
5³ = 125 cm³✓ (1)
5
Triangular prism: base 6, height 4, length 12 cm. Find the volume.
(3)
½(6)(4) = 12; 12 × 12 = 144 cm³✓✓✓ (3)
6
The diagram below shows a triangular prism whose cross-section is a right-angled triangle with sides of 15 cm and 8 cm. The prism is 5 cm long. Calculate the length of the third side of the triangle, and then the total surface area of the prism.
(5)
Third side = √(15² + 8²) = √289 = 17 cm (2)
Two ends = 2 × ½ × 15 × 8 = 120 cm² (1)
Three rectangles = (15 + 8 + 17) × 5 = 200 cm² (1)
SA = 120 + 200 = 320 cm² (1)✓✓✓✓✓ (5)
7
Cylinder radius 3 cm, height 7 cm. Find the volume (π ≈ 3,14).
(3)
3,14 × 9 × 7 = 197,82 cm³✓✓✓ (3)
8
Cylinder radius 3 cm, height 7 cm. Find the surface area (π ≈ 3,14).
(3)
2(3,14)(9) + 2(3,14)(3)(7) = 56,52 + 131,88 = 188,4 cm²✓✓✓ (3)
9
Cylinder radius 2 cm, height 5 cm. Find the volume (π ≈ 3,14).
(2)
3,14 × 4 × 5 = 62,8 cm³✓✓ (2)
10
How many mℓ does a container of 250 cm³ hold?
(1)
250 mℓ (1 cm³ = 1 mℓ)✓ (1)
11
A cylinder's height is doubled. What happens to its volume?
(2)
It doubles (height is not squared).✓✓ (2)
12
A cylinder's radius is doubled. What happens to its volume?
(2)
It becomes 4 times bigger (r is squared).✓✓ (2)

TOTAL: 31 marks