IGCSE Math B 6.G Similarity Topic Practice

Diagram NOT accurately drawn

In the diagram, XY is parallel to QR.
PXQ and PYR are straight lines.
$P Y=4 \mathrm{~cm}, Y R=6 \mathrm{~cm}, Q R=9 \mathrm{~cm}$.
Calculate the length of XY.

Diagram NOT accurately drawn.

The diagram shows triangle ABC.
D is a point on the line AC.
E is a point on the line BC.
BA is parallel to ED.

$$BC=10.8\text{ cm},\quad EC=8.1\text{ cm},\quad DE=3.6\text{ cm}$$

Work out the length, in cm to one decimal place, of BA.

Figure 1 shows a right circular solid cylinder with radius 5 cm and height 8 cm.

$\mathbf A$ and $\mathbf B$ are two mathematically similar solids.
The surface area of $\mathbf A$ is $3051\mathrm{cm}^2$.
The surface area of $\mathbf B$ is $5424\mathrm{cm}^2$.
Given that
$$\text{volume of }\mathbf A+\text{volume of }\mathbf B=2548\mathrm{cm}^3,$$
calculate the volume, in $\mathrm{cm}^3$, of $\mathbf B$.

10 A and B are two similar solids.
The surface area of the base of solid A is $324 \mathrm{~cm}^{2}$
The surface area of the base of solid B is $441 \mathrm{~cm}^{2}$
Given that the height of solid A is 9 cm, calculate the height of solid B.

Solid $\mathbf A$ and solid $\mathbf B$ are similar.
The surface area of solid $\mathbf A$ is $25\text{ cm}^2$.
The surface area of solid $\mathbf B$ is $900\text{ cm}^2$.
The volume of solid $\mathbf A$ is $50\text{ cm}^3$.
Calculate the volume, in $\text{cm}^3$, of solid $\mathbf B$.

Figure 2 shows the triangles ABE and ACD where B lies on AC and E lies on AD. The triangles are similar with $\angle A B E=\angle A C D$.

The area of quadrilateral BCDE is $18.9\text{ cm}^2$.
Calculate the length, in cm to 3 significant figures, of CD.

Here are two trapeziums.

\author{
Diagram NOT accurately drawn
}

The trapeziums ABCD and WXYZ are mathematically similar.
The area of trapezium ABCD is $36 \mathrm{~cm}^{2}$
Calculate the area of trapezium WXYZ.

A model of a ship is made to a scale of 3:400.
The surface area of the model is $7200\text{ cm}^2$.
Calculate, in $\text{m}^2$, the surface area of the ship.

There are $1000 \mathrm{~cm}^{3}$ of orange juice in a carton.
The total surface area of this carton is $700 \mathrm{~cm}^{2}$
For a special offer, a new carton is designed.
The volume of orange juice in the new carton is 33.1% more than the volume of orange juice in the original carton.
The new carton is mathematically similar to the original carton.
Calculate the total surface area of the new carton.

Figure 1 shows triangle OAB in which $\overrightarrow{O A}=4 \mathbf{a}$ and $\overrightarrow{O B}=8 \mathbf{b}$
P is the point on OA such that O P: O A=1: 4

The area of APQB is 150 cm².

Calculate the area of triangle OPQ.