Question

The cross-section of a prism is in the shape of a trapezium as shown.​

Answer 1

`Length = 15cm`

Explanation:

Given

The cross-section

`Volume = 630cm^3`

Required

Calculate the length

We start by calculating the area of the trapezium cross-section.

`Area = (1)/(2)(Sum\ of\ parallel\ sides) * Height`

`Area = (1)/(2)(9cm + 5cm) * 6cm`

`Area = (1)/(2)* 14cm* 6cm`

`Area = 42cm^2`

The length is then calculated from volume as:

`Volume = Area * Length`

Substitute values for Volume and Area

`630cm^3 = 42cm^2 * Length`

Make Length the subject

`Length = (630cm^3)/(42cm^2)`

`Length = 15cm`