A rectangular prism has a width of 92 ft and a volume of 240 ft². Find the volume of a similar prism with a width of 46 ft. Round to the nearest tenth, if necessary.
A.) 30 ft³
B.) 40 ft³
C.) 60 ft³
D.) 120 ft³
To find the volume of a similar prism, we need to use the concept of similarity.
Similar shapes have the same shape but different sizes. In this case, the rectangular prisms are similar, meaning they have the same shape but different dimensions.
Let's find the ratio of the widths of the two prisms to determine the relationship between their volumes.
The ratio of the widths is:
92 ft / 46 ft = 2
Since the ratio of the widths is 2, the ratio of the volumes will be the cube of the width ratio (since volume is related to the product of the three dimensions).
2^3 = 8
So, the ratio of the volumes of the two prisms is 8:1.
Now, let's find the volume of the second prism using the ratio. The volume of the first prism is given as 240 ft³.
Volume of the second prism = Volume of the first prism / Ratio of volumes
Volume of the second prism = 240 ft³ / 8 = 30 ft³
Hence, the volume of the similar prism with a width of 46 ft is 30 ft³.
Therefore, the answer is A.) 30 ft³.