Surface Area, Volume and Compound Shapes — Solutions

Full worked solutions, with method and final answer for every part.

Question 1

(a)Volume = πr²h.

π × 4² × 10 = 502.7 cm³ (3 s.f.)

Question 2

(a)Volume = (4/3)πr³.

(4/3)π × 6³ = 904.8 cm³ (3 s.f.)

Question 3

(a)Slant height uses Pythagoras: l = √(r² + h²). Volume = (1/3)πr²h.

l = √(3²+8²) = 8.54 cm; Volume = (1/3)π×3²×8 = 75.4 cm³

Question 4

(a)Volume of a cube = side³.

5³ = 125 cm³

(b)Surface area = 6 × side².

6 × 25 = 150 cm²

Question 5

(a)Volume of a prism = cross-sectional area × length.

12 × 10 = 120 cm³

Question 6

(a)Volume of hemisphere = (2/3)πr³.

(2/3)π(3³) ≈ 56.5 cm³ (3 s.f.)

Question 7

(a)Rectangle area = 8×5=40 cm². Semicircle radius=2.5, area=½πr²≈9.82 cm². Add together.

40 + 9.82 ≈ 49.8 cm² (3 s.f.)

Question 8

(a)Total SA = 2πr² + 2πrh = 2πr(r+h).

2π(3)(3+7) ≈ 188 cm² (3 s.f.)

Question 9

(a)Volume = (1/3)πr²h.

(1/3)π(5²)(12) ≈ 314 cm³ (3 s.f.)

Question 10

(a)Surface area = 4πr².

4π(4²) ≈ 201 cm² (3 s.f.)

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