Question

How do you work out the ratio of volume of the triangular prism to the volume of a cuboid?

Answer 1

Hint: We take arbitrary dimensions of the triangular prism and the cuboid. We find their formula for general volume measurement. Then we find the ratio of volume of the triangular prism to the volume of a cuboid.

Complete step by step solution:
We need to work out the ratio of volume of the triangular prism to the volume of a cuboid.
No particular data about the sides of the cuboid or the base of the prism have been given.
We will assume the dimensions of the figures and find the ratio.
First, we take the cuboid. We assume the dimensions for the cuboid is $a,b,c$ for length, breadth and height respectively.
We know the volume for cuboids is equal to the multiplication of three dimensions.
Therefore, the volume of the cuboid will be $abc$ cubic unit.

For the prism we need to know the base. We take the base area as $A$ and the height as $h$.
The volume of the prism becomes $A\times h=hA$ cubic unit.

The ratio of volume of the triangular prism to the volume of a cuboid becomes \[\dfrac{abc}{hA}\].
We now take an example.
Let the dimensions for the cuboid is $2,3,5$ units for length, breadth and height respectively.
Therefore, the volume of the cuboid will be $2\times 3\times 5=30$ cubic unit.
For the prism we need to know the base. We take the base area as $12$ unit and the height as $5$ unit.
The volume of the prism becomes $5\times 12=60$ cubic units.
The ratio is \[\dfrac{abc}{hA}=\dfrac{30}{60}=\dfrac{1}{2}\].

Note:
The base of the prism is fixed in this case as a triangle. A prism is a polyhedron in which all the faces are flat, and the bases are parallel to each other. It is a solid object with flat faces, identical ends, and the same cross-section along with its length.