a rectangular prism has a width of 92ft. and a volume of 240ft^3. Find the volume of a similar prism with a width of 23ft. Round to the nearest tenth if necessary.
a)3.8ft^3
b)60ft.^3
c)15ft.^3
d)10.4ft.^3
I am totally cinfused by this. Can somebody please help me? I would appreciate it. Thankss.
the volume of two "similar" shapes is proportional to the cubes of the corresponding sides
so if the new volume is V then
V/240 = 23^3/92^3
V = 240(12167)/778688
= 3.75
so it looks like a) is the correct answer
thank you Reiny!
That answer makes no sense though the width of the simmulair prism is already 23ft so 3.8ft^3 isn't a bigger number than 23ft also when you multiply the length and the height it will no were be 3.8^3 so good job stupid.
To solve this problem, we need to understand the concept of similar figures. Similar figures are figures that have the same shape but possibly different sizes.
In this case, we have two rectangular prisms that are similar. We know the width of the first prism is 92ft and its volume is 240ft^3. We need to find the volume of the second prism with a width of 23ft.
The volume of a rectangular prism is given by the formula:
Volume = length × width × height
Since the two prisms are similar, their corresponding sides are proportional. This means that the ratio of the widths is the same as the ratio of the volumes. In other words:
Volume of second prism / Volume of first prism = (Width of second prism / Width of first prism)^3
Let's plug in the given values:
Volume of second prism / 240ft^3 = (23ft / 92ft)^3
Now we can solve for the volume of the second prism by cross-multiplying:
Volume of second prism = 240ft^3 × (23ft / 92ft)^3
Calculate the expression on the right side to find the volume of the second prism:
Volume of second prism ≈ 240ft^3 × (0.25)^3
Volume of second prism ≈ 240ft^3 × 0.015625
Volume of second prism ≈ 3.75ft^3
Rounding to the nearest tenth, the volume of the similar prism with a width of 23ft is approximately 3.8ft^3.
Therefore, the answer is option a) 3.8ft^3.