The diagram represents a large cone of height 30 cm and base diameter 58 cm.

The large cone is made by placing a small cone A of height 10 cm and base diameter 5 cm on top of a frustum B.

(a)Calculate the volume of the frustum B.

Give your answer correct to 3 significant figures.

........................ cm3

(3 marks)

The diagram shows a frustum.

The diameter of the base is 3d cm and the diameter of the top is d cm. The height of the frustum is h cm.

The formula for the curved surface area, S cm2, of the frustum is

(b)Rearrange the formula to make h the subject.

h = ........................

(3 marks)

Two mathematically similar frustums have heights of 20 cm and 30 cm. The surface area of the smaller frustum is 450 cm2.

(c)Calculate the surface area of the larger frustum.

........................ cm2

(2 marks)

————————————————————————————————————————— Question 2

(a)Factorise 2x2 + 19x - 33(2 marks)

A cone fits exactly on top of a hemisphere to form a solid toy.

The radius, CA, of the base of the cone is 3 cm.

AB = 5 cm.

(b)Show that the total surface area of the toy is 33p cm2. (2 marks)

The radius of the base of a cylinder is x cm.

The height of the cylinder is 9.5 cm longer than the radius of its base.

The area of the curved surface of the cylinder is equal to the total surface area, 33p cm2, of the toy.

(c)Calculate the height of the cylinder.

.................. cm

(6 marks)

————————————————————————————————————————— Question 3

A tent has a groundsheet as its horizontal base.

The shape of the tent is a triangular prism of length 8 metres, with two identical half right-circular cones, one at each end.

The vertical cross-section of the prism is an isosceles triangle of height 2.4 metres and base 3.6 metres.

(a)Calculate the area of the groundsheet.

Give your answer, in m2, correct to one decimal place.(3 marks)

(b)Calculate the total volume of the tent.

Give your answer, in m2, correct to one decimal place.(4 marks)

————————————————————————————————————————— Question 4

A sphere has a radius of 5.4 cm.

A cone has a height of 8 cm.

The volume of the sphere is equal to the volume of the cone.

Calculate the radius of the base of the cone.

Give your answer, in centimetres, correct to 2 significant figures. (3 marks)

————————————————————————————————————————— Question 5

A cylinder has a height of 24 cm and a radius of 4 cm.

Work out the volume of the cylinder.

Give your answer correct to 3 significant figures.

........................ cm3

(2 marks)

————————————————————————————————————————— Question 6

AB is parallel to CD

Angle ACB = angle CBD = 90°.

Prove that triangle ABC is congruent to triangle DCB.(3 marks)

————————————————————————————————————————— Question 7

The diagram represents a large cone of height 6 cm and base diameter 18 cm.

The large cone is made by placing a small cone A of height 2 cm and base diameter 6 cm on top of a frustum B.

Calculate the volume of the frustum B.

Give your answer in terms of p.

...............................

(4 marks)

————————————————————————————————————————— Question 8

Triangle PQR is isosceles with PQ = PR.

X is a point on PQ.

Y is a point on PR.

PX = PY.

Prove that triangle PQY is congruent to triangle PRX.(3 marks)

————————————————————————————————————————— Question 9

The diagram shows a trapezium.

The measurements on the diagram are in centimetres.

The lengths of the parallel sides are x cm and 20 cm.

The height of the trapezium is 2x cm.

The area of the trapezium is 400 cm2.

(a)Show that

x2 + 20x = 400

(2 marks)

(b)Find the value of x.

Give your answer correct to 3 decimal places....