**8.2.1 Solid Geometry III, PT3 Practice**

Question 1:

Question 1:

The diagram below shows a cone with diameter 14 cm and height 6 cm.

Find the volume of the cone, in cm

^{3}.

*Solution:***Question 2:**

If the volume is 20 cm

^{2}, find the height of the pyramid, in cm.

Solution:Solution:

$\begin{array}{l}\text{Volume of a pyramid}=\frac{1}{3}\times \text{base area}\times h\\ \frac{1}{3}\times \text{base area}\times h=20\\ \frac{1}{3}\times 5\times 4\times h=20\\ \text{}\frac{20}{3}\times h=20\\ \text{}h=\overline{)20}\times \frac{3}{\overline{)20}}\\ \text{}h=3\text{cm}\end{array}$

**Question 3:**

Diagram below shows a composite solid consisting of a right circular cone, a right circular cylinder and a hemisphere.

The volume of the cylinder is 1650 cm

^{3}. Calculate the height, in cm, of the cone.

$\left[\text{Use}\pi =\frac{22}{7}\right]$

Solution:Solution:

$\begin{array}{l}\text{Volume of a cylinder}=\pi {r}^{2}h\\ \frac{22}{7}\times {r}^{2}\times 21=1650\\ \text{}{r}^{2}=\frac{1650\times 7}{22\times 21}\\ \text{}=25\\ \text{}r=5cm\\ \text{Thus the height of the cone}\\ =39-5-21\\ =13cm\end{array}$

**Question 4:**

The cross section of the prism shown is an isosceles triangle.

The volume of the prism, in cm

^{3}, is

Solution:Solution:

**Question 5:**

A right circular cone has a volume of 77 cm

^{3}and a circular base of radius 3.5 cm. Calculate its height.

Solution:Solution: