A box has a rectangular base UVXY with plane PQRS being vertically above UVXY as shown in the following figure.

If

1. The length of  and , Correct to one decimal place
2. The angle between the diagonal  and the base UVXY

The following figure represents a rectangular prism in which PQ =12 cm, QR=8cm and RY=4cm.

Find;

(i)The total surface area.

(ii)The angle between the planes PTZW and QRZW .

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

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

(i)     State the projection of  

(ii)  Name the angles between  

 The volume of a square pyramid is 28.2 cm³. If the sides of its base are 4 cm long, find the height of the pyramid correct to one decimal place.

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

(i)   The length of AH (give your answer correct to one decimal place).

 (ii)     The angle CAH.

  A rectangular box with top WXY Z and base ABCD has

AB = 9cm, BC = 12cm and WA = 3cm.

Calculate:

(i)  The length of AC ,

(ii)  The angle between WC and AC .

The figure below shows a tetrahedron. The length of each edge is 8cm. O is the centre of triangle ABC.

Calculate

(i)The length of VO

(ii)The angle between line AV and the plane ABC

Find the volume of a cone which has a base radius of 10 cm and slant height of 13 cm.

The following rectangular block is 8 cm long, 6 cm wide and 5 cm high.

(a) Name the angles formed between line AG with the planes ABCD and BCFG.

(b) Calculate:

the length of AC.

(ii) the length of AF. (iii) the size of angle CAF.

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

Calculate (i) The length AC (ii) The angle between WC and AC

VABCD is a pyramid with VA=VB=VC=VD=5cm and ABCD is a square base of sides 4cm each. Assume that the Centre of the base is at point N. Find

(i) The angle between VA and the base ABCD

(ii) The volume of the pyramid

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 such that

VA = VB = VC = VD = 6cm and AO = OC . Find:

(a) The angle VAD?

(b) The length of AC ?

(c) The angle between VA and the plane ABCD.

The volume of two similar cylinders is 125 cm³ and 512 cm³. If the radius of the larger cylinder is 8cm, find the radius of the smaller cylinder.

An open rectangular box measures externally 32cm long, 27cm wide and 15cm deep. If the box is made of wood 1cm thick, find the volume of wood used.