## Exam-Style Question on Mensuration## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 86. This question is similar to one that appeared on a IGCSE Extended paper in 2007. The use of a calculator is allowed.

[The surface area of a sphere of radius \(r\) is \(4\pi r^2\) and the volume is \(\frac43\pi r^3\)]

A solid metal sphere has a radius of 7.5 cm.

(a) Calculate the volume of the sphere to the nearest cubic centimetre.

(b) Calculate the surface area of the sphere to the nearest square centimetre.

(c) If one cubic centimetre of the metal has a mass of 4.9 grams calculate the mass of the sphere to three significant figures.

(d) Two of these spheres are placed in the water in a cylindrical tank with base diameter 32cm. Before they were lowered in the depth of the water was 19cm. Calculate the new depth of water in the cylinder when the spheres are fully submerged.

The worked solutions to these exam-style questions are only available to those who have a Transum Subscription. Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves. This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures. A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience. |

Drag this panel down to reveal the solution

If you need more practice try the self-checking interactive exercises called Surface Area and Volume.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.

Exam-Style Questions Main Page

To search the **entire Transum website** use the search box in the grey area below.

Do you have any comments about these exam-style questions? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

©1997 - 2020 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/