Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Chapter
Shape and Space 7
19 practice questions
Practice questions
1–10 of 19
Question 1
1 mark · Easy
Answer and see the solution →State one property that two similar triangles always have.
Question 2
2 marks · Easy
Answer and see the solution →A circle has a radius of 5 cm. The angle at the centre of a sector is 90°.
Calculate the length of the arc. Give your answer to 2 decimal places.
Question 3
2 marks · Easy
Answer and see the solution →Explain, using reasoning, why the volume of a cylinder increases if the height is doubled but the radius stays the same.
Question 4
3 marks · Easy
Answer and see the solution →The two pentagons below are similar. The side of the smaller pentagon is 4 cm. The side of the larger pentagon is 10 cm.
(a)[1 mark]Write down the scale factor for the sides from the smaller pentagon to the larger pentagon.
(b)[2 marks]If the area of the smaller pentagon is 13 cm², calculate the area of the larger pentagon.
Question 5
3 marks · Easy
Answer and see the solution →The table shows data for three sectors of a circle. The radius of all the sectors is 6 cm.
Sectors in a circle Sector Angle at Centre Arc Length (cm) A 60° B 120° C 180° Calculate and complete the missing arc lengths for sectors A, B, and C. Enter your answers to 2 decimal places.
Question 6
1 mark · Easy
Answer and see the solution →Write down the formula for the surface area of a sphere of radius .
Question 7
2 marks · Easy
Answer and see the solution →Triangle PQR is similar to triangle XYZ. The length PQ = 7 cm and the corresponding side XY = 14 cm. If the area of triangle PQR is 25 cm², find the area of triangle XYZ.
Question 8
2 marks · Normal
Answer and see the solution →Calculate the length of the arc of a circle with radius 7 cm and angle 45° at the centre.
Question 9
3 marks · Normal
Answer and see the solution →A closed cylindrical water tank has a diameter of 2 m and a height of 3.5 m.
Calculate:
(a)[2 marks]The volume of the tank. Give your answer in cubic metres.
(b)[1 mark]The total surface area of the tank (including top and bottom). Give your answer in square metres.
Question 10
3 marks · Normal
Answer and see the solution →Explain how you know that two triangles with sides in the ratio 2:3 are similar. Then, if the smaller triangle has an area of 8 cm², find the area of the larger triangle.