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Exam-Style Question on VolumeA mathematics exam-style question with a worked solution that can be revealed gradually |
Question id: 499. This question is similar to one that appeared on a GCSE Higher paper in 2019. The use of a calculator is not allowed.
The diagram, not drawn to scale, shows the plan for a large, three dimensional sign which has been ordered to hang outside an ice cream shop.
The sign is made of a hemisphere on top of a right cone.
The height of the cone is 2 m.
The top of the cone has a diameter of 1 m.
The hemisphere has a diameter of 1 m.
The total volume of the shape is \(k \pi \) cm3, where \(k\) is an integer.
Work out the value of k.
Where \(r\) is the radius of the sphere.
$$ \text{Volume of a cone} = \frac{\pi r^2 h}{3} $$Where \(r\) is the radius of the circular end of the cone and \(h\) is the height of the cone.
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