Surface Area and Volume: Complete Guide — Worksheet & Memo

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Grade 8 · Surface Area and Volume of 3D Objects

Surface Area and Volume: Complete Guide

MEMORANDUM

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/ 28

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 343 cm³. Determine the length of one edge, and hence the total surface area of the cube.
(4)
edge = ∛343 = 7 cm (2)
A cube has 6 square faces, so SA = 6 × 7² (1)
= 294 cm² (1)✓✓✓✓ (4)
2
Volume of a cube with side 4 cm (cube)
(1)
4³ = 64 cm³✓ (1)
3
Surface area of a cube with side 3 cm (cube)
(2)
6 × 9 = 54 cm²✓✓ (2)
4
Volume of a box 6 × 3 × 2 cm (box)
(2)
6 × 3 × 2 = 36 cm³✓✓ (2)
5
Surface area of a box 5 × 4 × 2 cm (box)
(3)
2[(5 × 4) + (5 × 2) + (4 × 2)] = 2(38) = 76 cm²✓✓✓ (3)
6
Volume of a box 10 × 5 × 4 cm (box)
(2)
200 cm³✓✓ (2)
7
Triangular prism: cross-section area 15 cm², length 8 cm. Volume? (prism)
(2)
15 × 8 = 120 cm³✓✓ (2)
8
Triangular prism: triangle base 8 cm, height 5 cm, length 10 cm. Volume? (prism)
(3)
1/2 × 8 × 5 = 20; 20 × 10 = 200 cm³✓✓✓ (3)
9
Triangular prism: the cross-section is a right-angled triangle with sides 6 cm, 8 cm and 10 cm, and the prism is 12 cm long. Calculate its total surface area. (prism)
(4)
Two triangles: 2 × 1/2 × 6 × 8 = 48 cm²
Three rectangles: (6 + 8 + 10) × 12 = 288 cm²
Total = 336 cm²✓✓✓✓ (4)
10
How many mℓ does a 200 cm³ container hold? (capacity)
(1)
200 mℓ✓ (1)
11
A box has volume 60 cm³, base 5 × 4 cm. Find the height. (reverse)
(2)
60 ÷ 20 = 3 cm✓✓ (2)
12
A cube has volume 125 cm³. Find its side length. (reverse)
(2)
∛125 = 5 cm✓✓ (2)

TOTAL: 28 marks