The prism has a volume of 70 mm3 find the volume of a scaled image with a scale factor of 3


What is a Prism?


In geometry, a prism is a polyhedron comprising an n-sided polygonal base, a set of identical parallel faces to the sides of the base, and n additional faces joining corresponding sides of the base. All bases and faces must be congruent., All vertices except for the two which join to form an n-sided polygonal face are an incident to exactly one face. A right prism is a prism in which the joining edges and faces are perpendicular to the base faces. This applies if the joining edges are joined perpendicularly to the corresponding faces. In contrast, if they are not perpendicular, it is called an oblique prism. A uniform prism is a right prism with all faces parallelograms.

The volume of any prism is V=Bh where B is the area of the base (which we call b for short).

How to calculate the volume of a Prism


First, you need to find the area of the base of the prism. To do this, you need to know the dimensions of the base. For this example, we’ll say the base is a rectangle with sides of 3 cm and 4 cm.

To find the area of a rectangle, you multiply the length by the width. So, in this case, the area of the base is 3 cm x 4 cm = 12 cm2.

Now that you know the area of the base, you can calculate the volume of the prism. To do this, you need to know two things:

The volume of a prism is equal to the area of the base multiplied by the height.
For our example prism, we’ll say that the height is 5 cm.
So, using our formula from above, we get: volume = 12 cm2 x 5 cm = 60 cm3

What is a scale factor?

A scale factor is a number which scales, or multiplies, some quantity. In the case of blueprints and models, a scale factor is used to represent a real object with a smaller or larger model or drawing. For example, if a blueprint has a scale factor of 1/4″ = 1′, this means that every quarter inch on the blueprint represents one foot in the real world. So, a line two inches long on the blueprint would represent eight feet (2 × 4) in the real world.

How to calculate the volume of a scaled image


You can calculate the volume of a scaled image by using the following formula:

Volume of scaled image = (Volume of original image) ÷ (Scale factor)³

For example, if you have an image that is 70 mm3 and you want to scale it up by a factor of 3, the volume of the scaled image would be:

Volume of scaled image = (70 mm3) ÷ (3)³

= 7,000 mm3


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