A rectangular prism has a width of 92ft. and a volume of 240ft cubed. find the volume of a similar prism with a width of 23ft.
I've been looking at this for a lonnggg time and I still cant figure it out. Can someone please explpain this for me?
the volume would be proportional to the cubes of the corresponding sides
so if the volume is x ft^3, then
x/240 = 23^3/92^2
cross-multiply and solve
<x/240 = 23^3/92^2 >
should be
x/240 = 23^3/92^3
60ft
To find the volume of a similar prism with a width of 23ft, we can use the concept of similarity. Similar shapes have proportional dimensions. In this case, we know that the width of the original prism is 92ft and its volume is 240ft³.
To find the scale factor between the two prisms, we can divide the width of the new prism (23ft) by the width of the original prism (92ft):
Scale factor = Width of new prism / Width of original prism
Scale factor = 23ft / 92ft
Scale factor = 0.25
Now, since the shapes are similar, we also know that the volumes will be proportional to the cube of the scale factor. Therefore, we can calculate the volume of the new prism:
Volume of new prism = Volume of original prism x (scale factor)³
Volume of new prism = 240ft³ x (0.25)³
Volume of new prism = 240ft³ x 0.015625
Volume of new prism = 3.75ft³
So, the volume of the similar prism with a width of 23ft is 3.75ft³.