The surface area of Cone A when the surface area of Cone B is 725 ft² for the case when Cone A is similar to Cone B with a scale factor of 3:5 is 2013.89 ft²
How does scale factor affects the area and volume of a figure?
Similar figure are zoomed in or zoomed out (or just no zoom) version of each other. They are scaled version of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.
So, if a side of a figure is of length L units, and that of its similar figure is of M units, then:
[tex]L = k \times M[/tex]
where 'k' will be called as scale factor.
The linear things grow linearly like length, height etc.
The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by [tex]k^2[/tex]
to get each other corresponding quantity from their similar figures' quantities.
- So area of first figure = [tex]k^2 \times[/tex] area of second figure
Similarly, increasing product derived quantities will need increased power of 'k' to get the corresponding quantity. Thus, for volume, it is k cubed. or
- Volume of first figure = [tex]k^3 \times[/tex] volume of second figure.
It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.
For this case, we're given that:
The scale factor between cone A and cone B is 3:5
That can be taken as: [tex]3/5 = 0.6[/tex] scale factor.
It means,
side length of cone A = [tex]0.6 \times[/tex] corresponding side length of cone B
Also, as given, we have:
Surface area of cone B = 725 ft²
Assume that cone A's surface area is S, then we get:
surface area of cone A = [tex]0.6^2 \times[/tex] surface area of cone B
[tex]725 = 0.6^2 \times S\\S =\dfrac{725}{0.6^2} \approx 2013.89 \: \rm ft^2[/tex]
Thus, the surface area of Cone A when the surface area of Cone B is 725 ft² for the case when Cone A is similar to Cone B with a scale factor of 3:5 is 2013.89 ft²
Learn more about scale factor here:
https://brainly.com/question/11178083
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