3. 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 23 ft. Round to the nearest tenth, if necessary. (1 point)
3.8 ft3
60 ft3
15 ft3
10.4 ft3
Please help me work this out! I'm not sure how to do this
volume=240ft^3 (23/92)^3=3.75
Round to nearest tenth.
3.8?
yes...
volume
The answer is 60
To find the volume of the similar prism with a width of 23 ft, we can use the concept of similarity. Since the two prisms are similar, their corresponding sides are proportional.
To find the ratio of the widths between the two prisms, we divide the width of the first prism (92 ft) by the width of the second prism (23 ft):
Ratio of widths = 92 ft / 23 ft = 4
This means that every dimension of the second prism is 1/4 of the corresponding dimension of the first prism.
The volume of a rectangular prism can be found by multiplying its length, width, and height. Since we only know the width of the first prism, we need to find its length and height.
Given that the volume of the first prism is 240 ft^3, we can write the equation:
240 ft^3 = length * 92 ft * height
To solve for the length and height, we need another piece of information or equation. Without it, we cannot calculate the exact volume of the similar prism.
However, if we assume that the length and height of the first prism are the same, we can find their common value:
240 ft^3 = length * 92 ft * length
240 ft^3 = 92 ft^2 * length^2
length^2 = 240 ft^3 / (92 ft^2)
length^2 ≈ 2.6087 ft^3
length ≈ sqrt(2.6087) ft ≈ 1.6146 ft (rounded to four decimal places)
Now we can find the volume of the similar prism with a width of 23 ft using the proportional relationship:
Volume of second prism = (width^3 of second prism) * (length of second prism) * (height of second prism)
Volume of second prism = (23 ft)^3 * (1.6146 ft) * (1.6146 ft)
Volume of second prism ≈ 15 ft^3
Therefore, the volume of the similar prism with a width of 23 ft is approximately 15 ft^3. Therefore, the correct answer is 15 ft^3.