6.5.2 Volume of Three Dimensional Shapes, PT3 Practice

$\begin{array}{l}\text{Height of the}△=\sqrt{{10}^2-6^2}\\ =\sqrt{64}\\ =8cm\\ \\ \text{Volume of prism}\\ =\text{Area of cross section}\times \text{Length}\\ =\left(\frac{1}{\cancel{2}}\times {\cancel{12}}^6\times 8\right)\times 16\\ =768c{m}^3\end{array}$

$\begin{array}{l}V=\frac{1}{3}\pi r^{2}h\\ h=\frac{3V}{\pi r^2}\\ =\frac{3\times 77}{\frac{22}{7}\times 3.5\times 3.5}\\ =6\text{ cm}\end{array}$

Question 6:
Puan Rafidah wants to prepare a right circular cone shaped container in order to fill it with candies for her family Hari Raya Celebration. Diagram below shows the net of a right circular cone.

The circumference of the lid is 44 cm and its height is 24 cm.
Calculate the volume, in cm³ , of the container.
$\left[\pi =\frac{22}{7}\right]$

Solution:
$\begin{array}{l}2\pi r=44\\ 2\times \frac{22}{7}\times r=44\\ r=\frac{44}{2}\times \frac{7}{22}\\ r=7\text{ cm}\\ \text{Volume of cone}=\frac{1}{3}\pi r^{2}h\\ =\frac{1}{3}\times \frac{22}{7}\times 7^2\times 24\\ =1232{\text{ cm}}^3\end{array}$

Question 7:
A barrel contains 36 l of mineral water. ⅔ of the mineral water is mixed with 6 bottles of syrup, with a volume of 1.5 l each. The drink will be poured into a number of bottles with the same volume of 300 ml.
How many number of bottles needed?

Solution:
$\begin{array}{l}\text{Volume of mineral water}\\ =\frac{2}{3}\times 36l\\ =24l\\ \\ \text{Volume of syrup}\\ =6\times 1.5l=9l\\ \\ \text{Total volume}=24+9\\ =33l=33000ml\\ \\ \text{Number of bottles needed}\\ =\frac{33000}{300}=110\end{array}$