Printable · GCSE Foundation · ages 14-16

Geometry and measures worksheet — GCSE Foundation

Fifteen questions across the geometry and measures statements at Foundation tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.

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Geometry and measures worksheet — GCSE Foundation

Maths · GCSE Foundation · Geometry and measures · Calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.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.
(a)7 cm³
(b)70 cm³
(c)35 cm³
(d)140 cm³
2.A sector of a circle has radius 4 cm and angle 90°. Using π = 3.14, work out the area of the sector.
(a)3.14 cm²
(b)12.56 cm²
(c)6.28 cm²
(d)50.24 cm²
3.A running track has a straight section and a semicircular bend. The bend is a semicircle with radius 32 m. Work out the length of the curved part of the bend, to 1 decimal place. (Use π = 3.14.)
(a)201.0 m
(b)64.0 m
(c)100.5 m
(d)50.2 m
4.A sector of a circle has radius 9 cm and angle 120°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.
(a)56.5 cm
(b)37.7 cm
(c)9.4 cm
(d)18.8 cm
5.A right-angled triangle has a hypotenuse of 8 cm, and one of its shorter sides is 4 cm. Work out the size of the angle between that 4 cm side and the hypotenuse.
(a)90°
(b)45°
(c)30°
(d)60°
6.A sector of a circle has radius 15 cm and angle 216°. Using π = 3.14, work out the arc length of the sector.
(a)94.2 cm
(b)56.52 cm
(c)28.26 cm
(d)113.04 cm
7.Two straight lines PQ and RS cross at point O. Angle POR = 52°. Work out angle QOS.
(a)104°
(b)38°
(c)52°
(d)128°
8.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.
(a)94.2 cm³
(b)90 cm³
(c)282.6 cm³
(d)1130.4 cm³
9.A shop sells rice in packs of 250 g. Aisha buys 4 packs. Work out the total mass of rice she buys, in kilograms.
(a)1000 kg
(b)0.254 kg
(c)0.0625 kg
(d)1 kg
10.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?
(a)8.5
(b)10.5
(c)3.5
(d)14
11.A fan-shaped rug is in the shape of a sector of a circle with radius 4 m and angle 180°. It costs £4 per square metre to make. Using π = 3.14, work out the total cost of the rug.
(a)£50.24
(b)£25.12
(c)£200.96
(d)£100.48
12.A square has sides of length 7 cm. Work out its area.
(a)49 cm²
(b)21 cm²
(c)28 cm²
(d)14 cm²
13.A parallelogram has an area of 54 cm² and a base of 9 cm. Work out its perpendicular height.
(a)12 cm
(b)486 cm
(c)6 cm
(d)45 cm
14.A robotic arm's tip starts at the point (12.5, −4.25) on a grid measured in centimetres. It moves by the vector $(6.5 - 3.75)$ to pick up a component, then by the vector $(- 1.5 2.25)$ to place it. Work out the coordinates of the tip after both moves.
(a)(0.75, 11)
(b)(8.75, 2.25)
(c)(6.5, 3.75)
(d)(11, 0.75)
15.A sector of a circle has radius 6 cm and angle 60°. Work out the arc length of the sector, in terms of π.
(a)12π cm
(b)6π cm
(c)π cm
(d)2π cm

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