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4MA1/2FR Jan 2021, Question 4: Volume of a Prism

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2FR (Foundation) · Calculator · 7 marks

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The question, in short

Name three 3D shapes A, B and C, count faces and vertices of shape C, then find each brick's volume given a 54 cm³ prism.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (ai) · 1 mark

Give the mathematical name of shape A.

  1. 1The shape is a perfectly round 3D object with all points on its surface equidistant from the center.

AnswerSphere

Part (aii) · 1 mark

Give the mathematical name of shape B.

  1. 1The shape has a circular base and tapers smoothly to a single point (apex) not in the plane of the base.

AnswerCone

Part (aiii) · 1 mark

Give the mathematical name of shape C.

  1. 1The shape has two identical polygonal bases connected by rectangular faces. The cross-section is constant along its length.

AnswerPrism

Part (bi) · 1 mark

State how many faces shape C has.

  1. 1Shape C is a prism with two hexagonal bases.
  2. 2A hexagon has 6 sides, so there are 6 rectangular faces connecting the bases.
  3. 3Total faces = 2 (bases) + 6 (rectangular faces) = 8.

Answer8

Part (bii) · 1 mark

State how many vertices shape C has.

  1. 1Each hexagonal base has 6 vertices.
  2. 2There are two bases: top and bottom.
  3. 3Total vertices = 6 (top) + 6 (bottom) = 12.

Answer12

Part (c) · 2 marks

Using the 54 cm³ prism volume and the brick arrangement, work out the volume of one brick.

  1. 1Count the bricks: 9 on the front face, 2 deep, so 9 × 2 = 18 bricks
  2. 2Volume of each brick = 54 ÷ 18 = 3

Answer3

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