Geometry and measures worksheet — GCSE Foundation

1.The diagram shows the plan of the base layer of a solid built from identical cubes. A second layer of cubes is added on top, filling the entire base layer to a height of 2 cubes everywhere. Work out how many squares are visible in the plan view of this solid.

2.A wooden block is a cuboid measuring 2 cm by 10 cm by 15 cm. Work out the volume of the block.

3.A cylinder has a volume of 942 cm³ and a height of 12 cm. Using π = 3.14, work out the radius of the cylinder.

4.A garden shed is shaped like a triangular prism: two identical vertical triangular end walls (the gable ends), joined by a sloping rectangular roof and a vertical rectangular back wall. Looking at the shed from directly above (the plan view), what shape is seen?

5.A children's slide is built as a right-angled triangle: the vertical ladder side is 2.4 m, the horizontal base along the ground is 3.2 m, and the sloping slide is the third side. Work out the exact length of the sloping slide.

6.Point B is at (3, 5). It is reflected in the line y = 2. Work out the coordinates of the image of point B.

7.P is the point (3, 4) and Q is the point (6, 0). Work out the distance of each point from the origin, and write down which point is closer to the origin.

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

9.A locus is described as the set of points exactly 4 cm from a fixed point O. What shape is this locus?

10.In an isosceles triangle each of the two base angles is 46°. Work out the size of the angle at the apex.

11.A television cable runs in a straight line from the edge of a flat roof 20 m above the ground to a bracket on a wall 5 m above the ground. The horizontal distance between the roof edge and the bracket is 15 m. Work out the length of the cable. Give your answer to 1 decimal place.

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

13.In triangle ABC, angle A is 2x°, angle B is 3x° and angle C is 4x°. Work out the size of angle B.

14.A right-angled triangle has a hypotenuse of 10 cm. One of its other angles is 45°. Work out the exact length of one of the two shorter sides.

15.A solid has 6 faces and 8 vertices. Using the formula F + V − E = 2, work out how many edges it has.