Math Is Fun Forum

Seirye

Member

Registered: 2008-04-02

Posts: 2

Ratios of shapes?

Okay, so I've got a worksheet here of ratios of different shapes to various things such as their volume and altitude and such. First problem is:

1.) The corresponding edges of two similar triangular prisms are in the ratio of 5:3. What is the ratio of their volumes?

How would you go about solving this? What would you do if given the ratios of two trapezoid's areas, 1:9, and asked for the ratio of their altitudes?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Ratios of shapes?

There are 2 facts you need to know for this question:

- If you multiply all lengths of a shape by x, then you multiply its area by x².
- If you multiply all lengths of a solid by x, then you multiply its volume by x³.

Knowing those, the questions aren't too hard. Post again if you still need help.

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Why did the vector cross the road?
It wanted to be normal.

Kiruki

Guest

Re: Ratios of shapes?

Does that mean you multiply all sides added together, the perimeter, or each side individually?

Math confuses me to high hell, help appreciated.

Oh, and when you're multiplying all lengths of a solid, how does that work?

Sorry... Jsut a conmfused kid trying to do his homework x.x

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Ratios of shapes?

Each side individually. Another way of thinking about it is to enlarge the shape by scale factor x.
Here's an example:

Say you have a rectangle measuring 4cm by 5cm. Its area would then be 20cm².
Now take another rectangle, with each length double that of the first one.
It would be an 8cm by 10cm rectangle, and so have an area of 80cm².

You multiplied each length by 2, and as a result, the area got multiplied by 2² = 4.

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Why did the vector cross the road?
It wanted to be normal.