A rectangular prism has a width of 92 ft and a volume of 240 ft3. Find the volume of a similar prism with a width of 46 ft
Given:
Width of rectangular prism = 92 ft
Volume of rectangular prism = 240 ft^3
Width of similar prism = 46 ft
Let the length and height of the prism be l and h respectively.
Volume of rectangular prism = lwh
240 = 92lh
Dividing both sides by 92,
l = 240/92 = 60/23 ft
h = 240/(92 × 60/23) = 15/23 ft
The ratio of width of two similar prisms is 46/92 = 1/2
The ratio of their volumes is (1/2)^3 = 1/8
Let V be the volume of the similar prism.
V = (1/8) × 240 = 30 ft^3
Therefore, the volume of the similar prism with a width of 46 ft is 30 ft^3.