Скачать или смотреть 2017 Maths General 2 HSC Q18 Find volume of skip bin in the shape of a trapezoidal prism using V=Ah

Sample solution: © The Maths Studio (themathsstudio.net)
Source: © NSW Education Standards Authority

Disclaimer - This sample solution is intended as a guide only and does not necessarily represent the best way to answer the question, nor is there any guarantee of accuracy.
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Finding the volume (V) of a prism involves multiplying the area (A) of the prism's base by its height (h) i.e. V=Ah.

Here are the general steps:

1. *Identify the Base Shape:*
Determine the shape of the prism's base (e.g., rectangular, triangular).

2. *Calculate the Area of the Base:*
If the base is a rectangle, multiply the length by the width.
If the base is a triangle, use the formula for the area of a triangle: Area = 0.5*b*h.
For other shapes, use the appropriate formula for finding the area of the base.

3. *Determine the Height of the Prism:*
Identify the perpendicular distance between the two parallel bases of the prism. This is the height of the prism.

4. *Multiply the Base Area by the Height:*
Multiply the area (A) of the base (from step 2) by the height (h) of the prism (from step 3).
The formula for volume is V=Ah.

5. *Express the Volume in the Correct Units:*
Ensure that your final answer is in cubic units, as volume is a measure of three-dimensional space.

Let's say you have a rectangular prism with a length L of 4 cm, a width W of 3 cm, and a height H of 5 cm. The volume V would be calculated as follows:

V = L*W*H = 4*3*5 = 60 cubic centimetres.

This process is applicable to prisms of various shapes; you just need to adapt the base area calculation according to the shape of the prism's base.