Volume — Solutions

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1. Q1 — Volume of rectangular prisms

   Fluency
   • (a) V = 8 × 5 × 3 = 120 cm³.
   • (b) V = 12 × 9 × 4.5 = 486 cm³.

2. Q2 — Volume of cylinders

   Fluency
   • (a) V = π(16)(10) = 160π ≈ 502.65 cm³.
   • (b) V = π(42.25)(8) = 338π ≈ 1061.86 cm³.

3. Q3 — Volume of pyramids

   Fluency
   • (a) Base = 36 cm². V = ⅓ × 36 × 10 = 120 cm³.
   • (b) Base = 40 cm². V = ⅓ × 40 × 12 = 160 cm³.

4. Q4 — Volume of cones

   Fluency
   • (a) V = ⅓π(25)(9) = 75π ≈ 235.62 cm³.
   • (b) V = ⅓π(64)(15) = 320π ≈ 1005.31 cm³.

5. Q5 — Volume of spheres

   Fluency
   • (a) V = &frac43;π(216) = 288π ≈ 904.78 cm³.
   • (b) r = 5 m. V = &frac43;π(125) = (500/3)π ≈ 523.60 m³.

6. Q6 — Volume to capacity conversions

   Understanding
   • (a) 4500 cm³ = 4500 mL = 4.5 L.
   • (b) 1 m³ = 1 kL, so 2.8 m³ = 2.8 kL.
   • (c) 350 L × 1000 = 350 000 cm³.

7. Q7 — Rectangular swimming pool

   Understanding
   • (a) V = 15 × 8 × 1.5 = 180 m³.
   • (b) 1 m³ = 1 kL, so capacity = 180 kL.
   • (c) ¾ × 180 = 135 m³. Depth = 135 ÷ (15 × 8) = 1.125 m.

8. Q8 — Grain silo: cylinder with conical top

   Understanding
   • (a) V_cyl = π(9)(8) = 72π ≈ 226.19 m³.
   • (b) V_cone = ⅓π(9)(2) = 6π ≈ 18.85 m³.
   • (c) Total = 72π + 6π = 78π ≈ 245.04 m³.
   • (d) 1 m³ = 1 kL, so capacity ≈ 245.04 kL.

9. Q9 — Ice cream cone with hemisphere

   Problem Solving
   • (a) V_cone = ⅓π(12.25)(10) = (122.5/3)π ≈ 128.28 cm³.
   • (b) V_hemi = ⅔π(42.875) = (85.75/3)π ≈ 89.80 cm³.
   • (c) Total ≈ 128.28 + 89.80 = 218.08 cm³.
   • (d) 218.08 cm³ > 80 mL. Exceeds one 80 mL serving by about 2.7×.

10. Q10 — Water tank filling time and cost

    Problem Solving
    • (a) V = π(1.44)(2.5) = 3.6π ≈ 11.31 m³ = 11.31 kL.
    • (b) 90% × 11.31 = 10.179 m³. Time = 10.179 ÷ 0.6 ≈ 16.97 min = 16 min 58 sec.
    • (c) 11.31 kL × $2.80 = $31.67.