1
1 A cylinder with radius 6 cm and height h cm has the same volume as a sphere with radius 4.5 cm.
Find the value of h.
[The volume, V, of a sphere with radius r is .]
h = ................................................... [3]
[Total: 3]
Water flows at a speed of 20 cm/s along a rectangular channel into a lake.
The width of the channel is 15 cm.
The depth of the water is 2.5 cm.
Calculate the amount of water that flows from the channel into the lake in 1 hour.
Give your answer in litres.
................................................... litres [4]
2
[Total: 4]
A prism with a right-angled triangle as its cross-section has a volume of 1000 cm3.
Calculate the value of x.
x = ................................................... [4]
[Total: 4]
3
4 A sphere with radius x cm has a volume of 1000 cm3.
Calculate the value of x.
[The volume, V, of a sphere with radius r is .]
x = ................................................... [3]
[Total: 3]
5 A cone with radius x cm and slant height cm has a volume of 1000 cm3.
Calculate the value of x.
[The volume, V, of a cone with radius r and height h is .]
x = ................................................... [4]
[Total: 4]
4
6 A cone with height 14.8 cm has volume 275 cm3.
Calculate the radius of the cone.
[The volume, V, of a cone with radius r and height h is .]
................................................... cm [3]
[Total: 3]
7 A solid metal prism with volume 500 cm3 is melted and made into 6 identical spheres.
Calculate the radius of each sphere.
[The volume, V, of a sphere with radius r is .]
................................................... cm [3]
[Total: 3]
5
8
25°
5 cm
NOT TO
SCALE
15 cm
The diagram shows a wooden prism of height 5 cm.
The cross section of the prism is a sector of a circle with sector angle 25°.
The radius of the sector is 15 cm.
Calculate the total surface area of the prism.
Answer .............................. cm2 [5]
[Total: 5]
6
The diagram shows a sector of a circle of radius 8 cm.
The length of the arc PQ is 6.4 cm.
Find the area of the sector.
................................................... cm2 [4]
[Total: 4]
7
10
The diagram shows two sectors of circles with the same centre.
Calculate the shaded area.
................................................... cm2 [3]
[Total: 3]
8
11
The sector of a circle has radius 8.5 m and angle 76°.
Calculate the perimeter of the sector.
................................................... m [3]
[Total: 3]
12 A bag contains 15 000 cm3 of sand.
Some of this sand is used to completely fill a hole in the shape of a cylinder.
The hole is 30 cm deep and has radius 10 cm.
Calculate the percentage of the sand from the bag that is used.
................................................... % [3]
[Total: 3]
9
13
B
NOT TO
SCALE
8 cm
30°
O A
C
OAB is the sector of a circle, centre O, with radius 8 cm and sector angle 30°.
BC is perpendicular to OA.
Calculate the area of the region shaded on the diagram.
Answer ................................................... cm2 [5]
[Total: 5]
10
14 15.4 cm
NOT TO
SCALE
18.2 cm
62°
The diagram shows a trapezium.
The trapezium has one line of symmetry.
Work out the area of the trapezium.
................................................... cm2 [4]
[Total: 4]
11
15 The diagram shows a right-angled triangle ABC.
The area of this triangle is 30 cm2.
(a) Show that .
[3]
(b) Use factorisation to solve the equation .
x = .............................. or x = .............................. [3]
(c) Calculate BC.
BC = ................................................... cm [3]
[Total: 9]
