A container, in the form of a cone resting on its vertex, is full when 4.158 litres of water is poured into it. (a) If the radius of its base is 21 cm, (i) ...
Question 1 Report
A container, in the form of a cone resting on its vertex, is full when 4.158 litres of water is poured into it.
(a) If the radius of its base is 21 cm,
(i) represent the information in a diagram;
(ii) calculate the height of the container.
(b) A certain amount of water is drawn out of the container such that the surface diameter of the water drops to 28 cm. Calculate the volume of the water drawn out. (Take \(\pi\) = \(\frac{22}{7}\))
Answer Details
(a)(i) Diagram: a cone standing on its vertex (point downwards), base radius 21 cm at the top, water filling it to height \(h\).
(a)(ii) Height. \(4.158\) litres \(= 4158 \text{ cm}^3\).
\[\tfrac{1}{3} \times \tfrac{22}{7} \times 21^2 \times h = 4158\] \[\tfrac{1}{3} \times \tfrac{22}{7} \times 441 \times h = 462h = 4158 \Rightarrow h = 9 \text{ cm}\](b) When the surface diameter drops to 28 cm, the surface radius is 14 cm. By similar cones the remaining water height is
\[h' = 9 \times \frac{14}{21} = 6 \text{ cm}\]Volume remaining:
\[\tfrac{1}{3} \times \tfrac{22}{7} \times 14^2 \times 6 = \tfrac{1}{3} \times 616 \times 6 = 1232 \text{ cm}^3\]Volume drawn out \(= 4158 - 1232 = 2926 \text{ cm}^3\).
Download The App On Google Playstore
Everything you need to excel in your exams
