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

Question id: 120. This question is similar to one that appeared on a IGCSE Extended paper in 2014. The use of a calculator is allowed.

The three sides of an equilateral triangle are tangents to a circle of radius \(r\) cm. The sides of the triangle are each 10cm long.

(a) Calculate the value of \(r\).

The second diagram shows a box in the shape of a triangular prism of length 15cm.

The cross section is an equilateral triangle with sides of length 10cm.

(b) Calculate the volume of the box.

The box contains cookies. Each cookie is a cylinder of radius 2.8cm and height 5mm.

(c) Calculate the largest number of cookies that will fit in the box.

(d) Calculate the volume of one cookie in cubic centimetres.

(e) Calculate the percentage of the volume of the box not filled with cookies.

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