Frustum: surface area and volume

Sample Frustum: surface area and volume questions

A few of the 8 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.

1. Question 11 markGrade 3
   A hemisphere is a solid. Which statement describes a hemisphere? [1]
   Show the worked solution

   A hemisphere is half of a sphere, so it has one flat circular face and one curved surface. B1
2. Question 21 markGrade 4
   Which statement describes a frustum of a cone? [1]
   Show the worked solution

   A frustum is what remains when the top of a cone is cut off by a plane parallel to the base. B1
3. Question 33 marksGrade 7
   A frustum is made by removing a small cone from the top of a large cone, using a cut parallel to the base. The large cone has base radius $9\text{ cm}$

What are the common mistakes in Frustum: surface area and volume?

When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.

• Subtracts radii for height

  Subtracted the radii to get a height. The two cones are similar, so heights are in the same ratio as the radii.

• Uses large cone only

  Found only the curved surface area of the large cone. Subtract the curved surface area of the small cone that was removed.

• Assumes a smaller similar shape shares the same height (or other linear dimension) as the larger shape, instead of applying the correct scale-factor ratio between corresponding dimensions

  The small and large cones are similar (same shape, different size), so the ratio of heights must equal the ratio of radii - since the small cone's radius is half the large cone's, its height is also half: $\frac{1}{2}\times20=10$

Quick answers about Frustum: surface area and volume

How many Frustum: surface area and volume practice questions are there?

There are 8 self-marking IGCSE Maths questions on Frustum: surface area and volume, written for Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Extended tier. Each one is marked instantly and has a full worked solution.

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