Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Chapter
Shape and Space 7
19 practice questions
Practice questions
1–8 of 8 · Normal
Question 1
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 2
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 3
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.
Question 4
4 marks · Normal
Answer and see the solution →(a)[2 marks]A sector of a circle has a radius of 6 cm. The angle at the centre is 75°.
Calculate the length of the arc. Give your answer to 3 significant figures.
(b)[2 marks]Work out the area of the sector. Give your answer to 3 significant figures.
Question 5
4 marks · Normal
Answer and see the solution →The table shows the dimensions of three solid objects:
Solids Shape Key dimension(s) Unit Sphere r = 4 cm Cone r = 3, h = 7 cm Cylinder r = 2, h = 5 cm Complete the table below by calculating the volume and total surface area of each solid. Give all answers to 3 significant figures.
Question 6
2 marks · Normal
Answer and see the solution →The areas of two similar rectangles are 45 cm² and 125 cm². If the shorter side of the smaller rectangle is 5 cm, calculate the corresponding side of the larger rectangle.
Question 7
3 marks · Normal
Answer and see the solution →Calculate the area of the shaded region, which consists of a semicircle with diameter 10 cm and a rectangle 10 cm by 6 cm. The diameter of the semicircle coincides with one side of the rectangle. Give your answer to 3 significant figures.
Question 8
3 marks · Normal
Answer and see the solution →A solid has the same volume as a sphere with radius 2 cm. If the solid is a cube, what is the length of its side? Explain your steps.