Three dimensional figures questions | form four Basic Mathematics

A bucket UVSTnwas made from the cone URT such that its top radius is 12cm, bottom radius is 9cm and its depth (PQ) is 10cm.

1. Find the height QR of the cone VRS, using the fact that triangles PRT and QRS are similar.
2. Find the volume of the bucket , giving your answer in four significant figures.

The following figure represents a rectangular prism in which , and .

Find :

1. The total surface area.
2. The angle between the planes PTZW and QRZW.

Calculate the volume of a cone whose base radius is 12cm and slant height is 20cm. (Use )

A rectangular box with top WXYZ and base ABCD has AB=9cm, BC=12cm and WA=3cm.

Calculate :

1. The length of AC,
2. The angle between WC and AC.

Sketch a square pyramid whose base is PQRS, vertex is at W and centre is at N, then answer the questions that follow:

1. State the projection of on PQRS.
2. Name the angle between and the plane PQRS.

The volume of a square pyramid is 28.2cm². If the sides of its base are 4cm long, find the height of the pyramid correct to one decimal place.

In the following cuboid , AB=5cm, BC=12cm and BG=10cm. Calculate:

1. The length of AH (give your answer correct to one decimal place).
2. The angle CAH.

The figure below shows a rectangular prism in which =16cm, =12cm and =5cm.

Calculate

1. Its total surface area
2. The angle between and the plane ABCD
3. The volume in litres the prism can hold (1 litre=1000cm³)

The figure below shows a rectangular prism in which Ab=10cm, BC=8cm and calculate the length of DF (Leave your answer in surd form).

In figure 3, ABCD is a rectangle in which AB=3cm and BC=2cm. V is a point that VA=VB=VC=VD=6cm and AO=OC. Find:

1. The angle VAD;
2. The length of AC;
3. The angle between VA and the plane ABCD.