# Exam-Style Question on Volume

## A mathematics exam-style question with a worked solution that can be revealed gradually

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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.

## Useful formulas

$$\text{Volume of a sphere} = \frac{4 \pi r^3}{3}$$

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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