A rectangular prism has a width of 92 ft and a volume of 240 ft^3. Find the volume of a similar prism with a width of 23 ft. Round to the nearest tenth, it necessary.
I know the answer is 3.8 feet because I got it wrong. But why is that the answer. If you cab please help me figure it out
Thank you
Many parents do say Thank you. The math is difficult most days. This home on the other side of the screen does say," Thank you kindly.
A Family,
volume of similar solids is proportional to the cube of their corresponding sides
240/x = 92^3/23^3
240/x = 778688/12167
778688x = 12167(240)
x = 3.75 or 3.8 to the nearest tenth
Please help me with the question that I posted before this one. Thank you.
1D
2A
3A
4A
5B
6A LESSON 10 SIMILAR SOLIDS B UNIT 4 MEASUREMENT
like
Well, let's take a moment to clown around with the problem and figure it out!
So, we have a rectangular prism with a width of 92 ft and a volume of 240 ft^3. Now, if we want to find the volume of a similar prism with a width of 23 ft, we can use the concept of similar figures.
When two figures are similar, that means they have the same shape, but possibly different sizes. In this case, the two prisms are similar because they have the same shape (a rectangle) but different dimensions.
Now, there's a special property of similar figures that can help us find the relationship between their volumes. It's called the scale factor. The scale factor is the ratio of corresponding side lengths.
In this problem, we can find the scale factor by dividing the width of the first prism (92 ft) by the width of the second prism (23 ft):
Scale factor = 92 ft / 23 ft = 4
So, the scale factor is 4. This means that every dimension of the larger prism is 4 times the corresponding dimension of the smaller prism. Now, let's use this information to find the volume of the smaller prism.
Since the scale factor is 4, the volume of the smaller prism is 4 times smaller than the volume of the larger prism. So, we can calculate it like this:
Volume of smaller prism = (Volume of larger prism) / (scale factor)^3
= 240 ft^3 / (4^3)
= 240 ft^3 / 64
= 3.75 ft^3
Rounded to the nearest tenth, the volume of the smaller prism is approximately 3.8 ft^3.
So, the correct answer is indeed 3.8 feet. Don't worry, math can sometimes be a bit of a clown!
I hope this helps!
To find the volume of a similar prism, we need to understand the relationship between the volumes of similar shapes. When two shapes are similar, their corresponding sides have a constant ratio. In this case, the width of the original prism is 92 ft, and the width of the similar prism is 23 ft, which means the ratio of the widths is 92/23.
To find the ratio between their volumes, we need to cube the ratio of the widths since volume is a three-dimensional measure. So, (92/23)^3 will give us the ratio of the volumes.
Calculate the ratio: (92/23)^3 ≈ 14.59
Now, we know that the ratio between the volumes of the two prisms is approximately 14.59. Since the volume of the original prism is 240 ft^3, we can set up a proportion to find the volume of the similar prism.
240 ft^3 / 1 = x ft^3 / 14.59
Solving for x, we get:
x ft^3 ≈ 240 ft^3 / 14.59 ≈ 16.45 ft^3
Rounding to the nearest tenth, the volume of the similar prism with a width of 23 ft is approximately 16.5 ft^3.
It seems like the answer you provided, 3.8 feet, is incorrect. Double-check your calculations to ensure accuracy.