Mathematics, 29.07.2019 03:30 jjjxxcsenone1034

Aprism with a base area of 5 ft² and a height of 10 ft is dilated by a factor of 6/5 . what is the volume of the dilated prism? enter your answer, as a decimal, in the box.

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First, you must find the original volume of the prism by applying the following formula:

V1=HxB

V1 is the original volume of the prism.
H is the height of the prism (H=10 ft).
B is the base are of the prism (B=5 ft2)

So, the original volume is:

V1=HxB
V1=(10 ft)(5 ft2)
V1=50 ft2

When the prism is dilated by a factor of 6/5, its volume is:

V2=(V1)*(6/5)^3
V2=(50 ft³)*(6/5)^3
V2= 86.4 ft³

What is the volume of the dilated prism?

The answer is: 86.4 ft³

Answer from: zackcarlson9374

Step

Find the volume of the original prism

we know that

the volume of the prism is equal to

V=Bh

where

B is the area of the base of the prism

h is the height of the prism

in this problem we have

$B=5\ ft^{2}\\h=10\ ft$

substitute in the formula of volume

$V=5*10=50\ ft^{3}$

Step

Find the volume of the dilated prism

we know that

$volume\ of\ the\ dilated\ prism=[scale\ factor^{3}]*volume\ of\ the\ original\ prism$

we have

$scale\ factor=\frac{6}{5}$

$volume\ of\ the\ original\ prism=50\ ft^{3}$

substitute the values

$volume\ of\ the\ dilated\ prism=(\frac{6}{5})^{3}*50$

$volume\ of\ the\ dilated\ prism=1.728*50\\ \\volume\ of\ the\ dilated\ prism=86.4\ ft^{3}$

therefore

the answer is

the volume of the dilated prism is $86.4\ ft^{3}$

Answer from: Quest

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

Me if you can and if you finished this lesson on edg- comment you.

Answer from: Quest

yes

yes yes yes

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Aprism with a base area of 5 ft² and a height of 10 ft is dilated by a factor of 6/5 . what is the v...

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