Two cubes are placed next to each other. The length of each of the edges of the larger cube is $4 \mathrm{~cm}$. If the ratio of their surface areas is $1: 4$, calculate:

a the surface area of the small cube,

b the length of an edge of the small cube.

https://cdn.mathpix.com/snip/images/0KLgQSqtWLyeuB5Zs-UIBiLI1p6kQ9lNh3yGo3Sx5zY.original.fullsize.png

If the wheel of a bicysele has a diameter of 60 cm, calculate how far a cyclist will have travelled after the wheel has rotated 100 times.

A circular ring has a cross-section as shown (left). If the outer radius is 22mm and the inner radius 20mm, calculate the cross-sectional area of the ring.

Two buildings on opposite sides of a street are $40 \mathrm{~m}$ apart. From the top of the taller building, which is $185 \mathrm{~m}$ high, the angle of depression to the top of the shorter building is $13^{\circ}$. Find the height of the shorter building.

Two observers are 400 ft apart on opposite sides of a tree. The angles of elevation from the observers to the top of the tree are 15° and 20° .Find the height of the tree.

The angle of elevation from a ship to the top of a lighthouse is

$$4 ^ { \circ }$$

If the top of the lighthouse is known to be 50 m above sea level, how far is the ship from the lighthouse?

An ice cream consists of a hemisphere and a cone (right). Calculate, in exact form, its total volume.

https://cdn.mathpix.com/snip/images/N7o0ZOC0uGqqXs_OavtIvxZI3fma3DiaHJLyMWSQQkw.original.fullsize.png

A rotating sprinkler is placed in one corner of a garden (below). If it has a reach of $8 \mathrm{~m}$ and rotates through an angle of $30^{\circ}$, calculate the area of garden not being watered. Give your answer in terms of $\pi$.

https://cdn.mathpix.com/snip/images/0i5m1R2vIe9gKh4nc_-IHaKq58xnWDP_VZz5cB6unWc.original.fullsize.png

The triangle ADE shown has an area of 12 $\mathrm{cm}^2$.

a Calculate the area of triangle ABC.

b Calculate the length BC.

Calculate the number of sides a regular polygon has if an interior angle is five times the size of an exterior angle.

The interior angles of regular polygons are given below. In each case calculate the number of sides the polygon has. a) $108^{\circ}$ b) $150^{\circ}$ c) $162^{\circ}$ d) $156^{\circ}$ e) $171^{\circ}$ f) $179^{\circ}$

Calculate the perpendicular height $h \mathrm{~cm}$ for the pyramid, given that it has a volume of $168 \mathrm{~cm}^3$.

https://cdn.mathpix.com/snip/images/XfaZY5cdyT-x8jZN_AvmW05RTg5ts3ccqCFYjdslQHw.original.fullsize.png

Calculate the perimeter of each of these shapes. Give your answers in exact form.

https://cdn.mathpix.com/snip/images/B7yiNYObiOHLt5zvGqmWh9j9L0g36WOXt_KrL3QiO1Q.original.fullsize.png

A cuboid has dimensions as shown in the earlier diagram : If the cuboid is enlarged by a scale factor of 2.5, calculate:
a) the total surface area of the original cuboid b) the total surface area of the enlarged cuboid c) the volume of the original cuboid d) the volume of the enlarged cuboid.