1. (a) Volume = base × height × length |
(b) Volume = Area of triangle x length |
(c) Volume = Area of circle x height |
(d) Volume = Area of cuboid + Area of triangular prism |
2.(a) Volume = 3 × 4 × 0.5 = 6 m3
(b) 3 m = 300 cm , 4 m = 400 cm, 0.5 m = 50 cm
Volume = 300 × 400 × 50 = 6 000 000 cm3
(c) Surface area = 2 × (3 × 4 + 3 × 0.5 + 4 × 0.5) = 31 m2
3. Volume of solid = Area × length
= (7 × 10 − 3 × 3) × 4 = 244 cm3
4. (a) Volume of tank = 3 × 2 × 4 = 24 m3
(b) Surface area = 3 × 2 + 2 × (2 × 4 + 3 × 4) = 46 m2
5. (a) Surface area = 2 × (8 × 4 + 4 × 3 + 3 × 8) |
(b) Surface area = Area of circle × height |
= 1/3 × π 32 × 8 = 75.4 cm3 (to 3 s.f.)
7. Volume of sphere = 4/3πr3
= 4/3 . 3.14 . 43 = V = 268 cm3 (to 3 s.f.)
Surface area = 4πr2
= 4 . 3.14 . 42 = 201 cm2 (to 3 s. f.)
8. Using Pythagoras' Theorem r2 = 172 − 152
r = 8 cm,
Volume = 1/3πr2h =
1/3 × 3.14 × 82 × 15 = 1000 cm3 (to 3 s. f.)
Surface area = πrl + πr2 = 3.14 × 8 × 17 + 3.14 × 82
= 628 cm2 (to 3 s. f. )
9. Volume of a cylinder = πr2 h
5.5 = 3.14 × r2 .7
r = 0.500 m (to 3 s.f.)
10. (a) Volume of pool = 0.5 (1.5 + 3) × 10 × 5
= 112.5 m3
(b) Surface area of inside of pool = 5 × 3 + 1.5 × 5 + 11 × 5 + 2 × 0.5 × (1.5 + 3) × 10
= 122.5 m2
(c) Cost of paint = 3 × 122.5/50 × 40 = $294