[3 marks sum]

Question 13 Marks

Two similar cylindrical tins have base radii of 6 cm and 8 cm respectively. Find the capacity of the smaller tin, if the capacity of the larger tin is $256 \mathrm{~cm}^3$.

Answer

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Question 23 Marks

Two similar jugs have heights of 4 cm and 6 cm respectively. If the capacity of the smaller jug is $48 \mathrm{~cm}^3$, find the capacity of the larger jug.

Answer

Self

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Question 33 Marks

The model of a building is constructed with scale factor $1: 30$.
(i) If the height of the model is 80 cm , find the actual height of the building in metre.
(ii) If the actual volume of the tank on the top of the building is $27 \mathrm{~m}^3$, find the volume of the tank on the top of the model.

Answer

Self

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Question 43 Marks

Two bottles of sauce of circular cross-section are completely similar in every respect. One is 24 cm high and the other is 32 cm high.
(i) Calculate the external diameter of the smaller bottle, given that the corresponding diameter for the other bottle is 8 cm .
(ii) The smaller bottle can hold $270 \mathrm{~cm}^3$ of sauce. How much sauce can the bigger bottle hold?

Answer

Self

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Question 53 Marks

The surface area of a solid is $5 \mathrm{~m}^2$, while the surface area of its model is $20 \mathrm{~cm}^2$. Find.
(i) the scale factor
(ii) the volume of the solid if the volume of the model is $100 \mathrm{~cm}^3$.

Answer

Self

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Question 63 Marks

In the map of a rectangular plot of land the length $=2.5 \mathrm{~cm}$ and breadth $=1.4 \mathrm{~cm}$. If the scale is $1: 10000$, then find the area of the plot in $\mathrm{m}^2$.

Answer

Self

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Question 73 Marks

A rectangle having an area of $60 \mathrm{~cm}^2$ is transformed under enlargement about a point in space. If the area of its image is $135 \mathrm{~cm}^2$, find the scale factor of the enlargement.

Answer

Self

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Question 83 Marks

$\triangle \mathrm{ABC}$ is reduced by a scale factor 0.72 . If the area of $\triangle \mathrm{ABC}$ is $62.5 \mathrm{~cm}^2$, find the area of the image.

Answer

Self

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Question 93 Marks

$\triangle \mathrm{ABC}$ with sides $\mathrm{AB}=12 \mathrm{~cm}, \mathrm{BC}=8 \mathrm{~cm}$ and $\mathrm{AC}=14 \mathrm{~cm}$ is enlarged to $\Delta \mathrm{A}^{\prime} \mathrm{B}^{\prime} \mathrm{C}^{\prime}$ such that the smallest side of $\Delta \mathrm{A}^{\prime} \mathrm{B}^{\prime} \mathrm{C}^{\prime}$ is 12 cm . Find the scale factor and use it to find the length of the other sides of the image $\Delta A^{\prime} B^{\prime} C^{\prime}$.

Answer

Self

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Mathematics [3 marks sum]

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