Geometry and measures worksheet — GCSE Foundation

1.A sector of a circle has radius 15 cm and angle 216°. Using π = 3.14, work out the arc length of the sector.

2.A cylindrical water tank has a solid hemispherical dome on top, both with radius 2 m. Work out the volume of the hemispherical dome alone. Use π = 3.14 and give your answer correct to 3 decimal places.

3.A circular garden pond has a diameter of 5 m. A gardener is laying gravel around it in a ring-shaped path 1 m wide, measured outward from the edge of the pond. Work out the area of the gravel path. Use π = 3.14.

4.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.

5.A trapezium has an area of 45 cm², a perpendicular height of 5 cm, and one parallel side of length 10 cm. Work out the length of the other parallel side.

6.A rectangle has vertices A(0, 0), B(6, 0), C(6, 4) and D(0, 4). Work out the length of the diagonal AC. Give your answer correct to 2 decimal places.

7.Three angles meet at a single point on one side of a straight line. Two of the angles are 48° and 65°. Work out the third angle.

8.A sector of a circle has radius 12 cm and angle 45°. Using π = 3.14, work out the area of the sector.

9.A solid rubber ball has a radius of 3 cm. Work out the volume of the ball. Use π = 3.14.

10.A sector of a circle has radius 9 cm and angle 40°. Work out the area of the sector, in terms of π.

11.A footpath is 3750 m long. Work out this distance in kilometres.

12.A submarine travels due south. What is the three-figure bearing for this direction?

13.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.

14.Triangle JKL has a right angle at K, hypotenuse JL = 13 cm, and side JK = 5 cm. Triangle MNO has a right angle at N, hypotenuse MO = 13 cm, and side MN = 5 cm. Using only the facts given, and without working out any further lengths, write down the congruence condition that proves triangle JKL is congruent to triangle MNO.

15.Two straight lines PQ and RS cross at point O. Angle POR = 52°. Work out angle QOS.