SPM Mathematics Trial 2024 (Selangor Set 2), Paper 2 (Question 11)

Question 11:
Puan Lim invited 150 guests for an open house in conjunction with Chinese New Year celebration. Diagram 7 showed a cylindrical water container that has been fully filled with drinks and hexagonal glass prepared by Puan Lim.


(a) Puan Lim orders her daughter to fill the glass with drinks three quarter full to serve their guests. If every guest refills their drink five times, is the volume of drink in the container enough to accommodate the needs? Using π = 22/7, justify your answer. [5 marks]

(b) Half an hour after the celebration started, Puan Lim found out that the water container has a leakage. The rate of water dripped out was 0.7 cm³ per second. Calculate the percentage of volume of water that dripped out. [4 marks]

Solution:
(a)
$$\text { Volume of cylinder, } \begin{aligned} V_A & =\pi r^2 h \\ & =\frac{22}{7} \times 25^2 \times 68 \\ & =133571 \frac{3}{7} \mathrm{~cm}^3 \end{aligned}$$
Volume of 150 hexagon shaped glass with ¾ full and refills with 5 times, V_B
$$\begin{aligned} & =150 \times \frac{3}{4} \times \text { Base area } \times \text { height } \times 6 \\ & =150 \times \frac{3}{4} \times 15.8 \times 14 \times 6 \\ & =149310 \mathrm{~cm}^3 \end{aligned}$$

V_A < V_B
Thus, the volume of drink in the container is not enough to accommodate the needs of the guests.

(b)
$$\begin{aligned} &\text {Volume of water dripping out}\\ &\begin{aligned} & =0.7 \times\left(\frac{1}{2} \times 60 \times 60\right) \text { second } \\ & =1260 \mathrm{~cm}^3 \end{aligned} \end{aligned}$$
$$\begin{aligned} &\text {Percentage of volume of water dripped out}\\ &\begin{aligned} & =\frac{1260}{133571 \frac{3}{7}} \times 100 \% \\ & =0.94 \% \end{aligned} \end{aligned}$$