1. (a) Volume = base × height × length= 12 × 4 × 6 = 288 cm3 (b) Volume = Area of triangle x length= (0.5 × 5 × 6) × 8 = 120 m3 (c) Volume = Area of circle x height= (π × 62) × 20 = 2260 cm3 (d) Volume = Area of cuboid + Area of triangular prism= 5 × 6 × 8 + 0.5 × 6 × 3 × 8 = 312 m3

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)= 136 cm2 (b) Surface area = Area of circle × height= 2πr 2 + 2πr l= 2π7 2 + 2π7.9 = 703 mm2 (to 3 s.f.)

= 1/3 × π 3× 8 = 75.4 cm(to 3 s.f.)

7. Volume of sphere = 4/3πr3
= 4/3
. 3.14 4V = 268 cm3 (to 3 s.f.)

Surface area = 4πr2
= 4 . 3.14 42 = 201 cm(to 3 s. f.)

8. Using Pythagoras' Theorem r= 17− 152
r = 8 cm,
Volume = 1/3πr
2h =
1/3 × 3.14 × 8
2 × 15 = 1000 cm(to 3 s. f.)

Surface area = πrl + πr2 = 3.14 × 8 × 17 + 3.14 × 82
628 cm(to 3 s. f. )

9. Volume of a cylinder = πrh
5.5 = 3.14 × r
2 .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