Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Chapter
Shape and Space 7
19 practice questions
Practice questions
11–19 of 19
Question 11
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 12
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 13
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 14
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 15
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.
Question 16
2 marks · Hard
Answer and see the solution →A sector of a circle has a radius of 10 cm. The angle at the centre is 72°. Calculate the area of the sector. Give your answer to 3 significant figures.
Question 17
4 marks · Hard
Answer and see the solution →A closed cone has a base radius of 6 cm and a perpendicular height of 8 cm.
(a)[1 mark]Calculate the slant height of the cone. Give your answer to 3 significant figures.
(b)[3 marks]Calculate the total surface area of the cone. Give your answer to 3 significant figures.
Question 18
4 marks · Hard
Answer and see the solution →Two solid spheres are similar. The surface area of the smaller sphere is 48 cm² and the surface area of the larger sphere is 192 cm².
(a)[2 marks]Explain how you would find the ratio of the radii of the two spheres.
(b)[2 marks]Using your answer to (a), work out the ratio of the volumes of the smaller sphere to the larger sphere.
Question 19
2 marks · Hard
Answer and see the solution →Find the length of the arc of a circle with radius 12 cm and angle 40° at the centre. Give your answer to 2 decimal places.