(a) A cone has base diameter 8 cm and perpendicular height 15 cm.
(i) Calculate the volume of the cone.
(ii) A label completely covers the curved surface area of the cone. Calculate the area of the label as a percentage of the total surface area of the cone.
(b) An empty cylindrical container has radius 0.45 m. 300 litres of water is poured into the container at a rate of 375 ml per second.
(i) Find the time taken, in minutes and seconds, for all the water to be poured into the container.
(ii) Calculate the height of the water in the container.
(a)(i) 251 or 251.3 to 251.4 cm³
Using V = (1/3)πr²h with r=4cm, h=15cm → V ≈ 251.3 cm³
(a)(ii) 79.5 or 79.51%
1. Find slant height (l) = √(4²+15²) ≈ 15.52cm
2. Curved area = π×4×15.52 ≈ 201.1cm²
3. Total area = 201.1 + π×4² ≈ 226.2cm²
4. Percentage = (201.1/226.2)×100 ≈ 79.5%
(b)(i) 13 min 20 sec
1. Convert 300L → 300,000ml
2. Time = 300,000 ÷ 375 = 800 seconds
3. Convert to minutes: 800÷60 = 13min 20sec
(b)(ii) 0.472 or 0.4715 to 0.4716 m
1. Convert 300L → 0.3m³
2. Using V = πr²h → 0.3 = π×(0.45)²×h
3. Solve for h ≈ 0.4715m
