a right hexagonal prism is enlarged by a scale factor of 5.7
a)determine the value of volume of large prism/volume of small prism. do not round answer.. how do i figure this out?
the volume of two similar solids is proportional to the cube of corresponding sides.
So if one side is 1, then the corresponding side of the larger is 5.7
volume larger/volume of smaller = 5.7^3/1^3
= 185.193 : 1
To determine the value of the volume of the large prism divided by the volume of the small prism after enlargement, you need to analyze the relationship between the volumes and the scale factor.
The volume of a right hexagonal prism is given by the formula:
V = (3√3 / 2) * a^2 * h
Where:
a = apothem or side length of the base
h = height of the prism
Since the scale factor is 5.7, we can represent the new dimensions as:
a' = 5.7a
h' = 5.7h
Now, let's assume the volume of the small prism is V1, and the volume of the enlarged prism is V2.
V1 = (3√3 / 2) * a^2 * h
V2 = (3√3 / 2) * (5.7a)^2 * (5.7h)
To find the value of V2/V1, we can divide the equations:
V2/V1 = [(3√3 / 2) * (5.7a)^2 * (5.7h)] / [(3√3 / 2) * a^2 * h]
Simplifying:
V2/V1 = (5.7a)^2 * (5.7h) / (a^2 * h)
= (5.7^2 * a^2 * 5.7 * h) / (a^2 * h)
= 5.7^2 * 5.7
= 5.7^3
Therefore, the value of V2/V1 is equal to 5.7^3.
To determine the value of the volume of the large prism divided by the volume of the small prism, you need to understand the relationship between the volumes of similar shapes.
When a shape is enlarged by a scale factor, the ratio of the volumes of the enlarged shape to the original shape is equal to the cube of the scale factor.
In this case, the right hexagonal prism is enlarged by a scale factor of 5.7, so the ratio of the volumes would be (5.7)^3 = 183.333 (approximate value).
Therefore, the value of the volume of the large prism divided by the volume of the small prism is 183.333 (approximate value).