Geometry and measures worksheet — GCSE Foundation

1.Loose sweets are sold at £1.20 per 100 g. Work out the cost of 350 g of sweets.

2.An ice cream is made from a cone of radius 3 cm and height 10 cm, topped with a hemisphere of the same radius sitting exactly on top of the cone. Work out the total volume of the ice cream. Use π = 3.14. Give your answer to the nearest whole number. Volume of a cone = 1/3 × πr²h. Volume of a sphere = 4/3 × πr³.

3.A sector of a circle has an angle of 90° and an arc length of 15.7 cm. Using π = 3.14, work out the radius of the circle.

4.A cylinder has a radius of 3 cm and a height of 10 cm. Using π = 3.14, work out the volume of the cylinder.

5.A furniture catalogue drawing uses a scale of 1 cm to 1.5 m. A sofa in the drawing is measured as 7 cm long. What is the real length of the sofa, in metres?

6.A warehouse stores identical cube-shaped crates. Its plan view is a 2 by 4 rectangle of crate positions, and every position is filled to a height of 3 crates, except one corner position, which has only 2 crates stacked on it because a delivery was incomplete. How many crates are there in total?

7.A birthday cake is a cylinder of radius 10 cm and height 8 cm, with a thin ribbon fixed exactly once around the curved side, at half the height, and joined with no overlap. Work out the length of ribbon needed. Use π = 3.14.

8.A sector of a circle has radius 6 cm and an arc length of 15.7 cm. Using π = 3.14, work out the angle of the sector.

9.A triangular prism has a cross-section that is a triangle with a base of 3.5 cm and a perpendicular height of 4 cm. The prism is 10 cm long. Work out the volume of the prism.

10.A shop sells rice in packs of 250 g. Aisha buys 4 packs. Work out the total mass of rice she buys, in kilograms.

11.Write down which quadrant contains the point (−3, 5) when plotted on a coordinate grid.

12.Two angles lie on a straight line. One angle is 37°. Work out the size of the other angle.

13.A cylinder has a radius of 5 cm. Its volume is 471 cm³. Using π = 3.14, work out the height of the cylinder.

14.A triangular sail for a small boat has a base of 2.4 m and a height of 1.75 m. Sailcloth costs £12.50 per m². Work out the total cost of the sailcloth needed for the sail.

15.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?