A rectangular prism has a width of 92 ft and a volume of 240 ft find the volume of a similar prism with a width of 46 ft
The volume of the similar prism with a width of 46 ft is 120 ft.
To solve this problem, we can use the concept of similarity between the two rectangular prisms.
Similar objects have proportional dimensions. In other words, corresponding sides of similar objects are in the same ratio.
Let's set up a proportion to find the ratio of the volumes of the two prisms.
The ratio of the widths of the two prisms is 46/92 = 1/2 since the width of the second prism is half the width of the first prism.
However, the volume of a rectangular prism is given by the formula: Volume = length x width x height.
Since we are only changing the width and need to find the new volume, we can multiply the original volume by the square of the width ratio.
Let's calculate the volume of the smaller prism:
Volume of the smaller prism = Volume of the larger prism x (width ratio)^2
= 240 ft^3 x (1/2)^2
= 240 ft^3 x 1/4
= 60 ft^3
Therefore, the volume of the similar prism with a width of 46 ft is 60 ft^3.
To find the volume of a similar rectangular prism, we can use the concept of ratios.
The ratio of the width of the original prism to the width of the similar prism is 92:46, which simplifies to 2:1.
Since the volume of the original prism is 240 ft³, we can determine the volume of the similar prism by applying the ratio to the volume.
2:1 is the same as saying 2/1, so we need to multiply the volume of the original prism by the ratio 2/1.
Volume of the similar prism = Volume of the original prism x 2/1
= 240 ft³ x 2/1
= 480 ft³
Therefore, the volume of the similar prism with a width of 46 ft is 480 ft³.