Please help!! Which of the following could represent the scale factor of the smaller figure to the larger figure?
2 answers:
Answer:
Scale factor is 216 : 343
Step-by-step explanation:
To find the scale factor of smaller figure to the larger figure means we have to find the ratio of smaller figure as compared to the smaller one.
To find the ratio we will divide the volume of smaller figure by larger one.
Scale factor =
Or in simple way ratio is 216 : 343
Therefore scale factor 216 : 343 will be the answer.
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Answer:
The width of the box is 6.7 cm
The maximum volume is 148.1 cm³
Step-by-step explanation:
The given parameters of the box Jorge is asked to build are;
The maximum girth of the box = 20 cm
The nature of the sides of the box = 2 square sides and 4 rectangular sides
The side length of square side of the box = w
The length of the rectangular side of the box = l
Therefore, we have;
The girth = 2·w + 2·l = 20 cm
∴ w + l = 20/2 = 10
w + l = 10
l = 10 - w
The volume of the box, V = Area of square side × Length of rectangular side
∴ V = w × w × l = w × w × (10 - w)
V = 10·w² - w³
At the maximum volume, we have;
dV/dw = d(10·w² - w³)/dw = 0
∴ d(10·w² - w³)/dw = 2×10·w - 3·w² = 0
2×10·w - 3·w² = 20·w - 3·w² = 0
20·w - 3·w² = 0 at the maximum volume
w·(20 - 3·w) = 0
∴ w = 0 or w = 20/3 = 6.
Given that 6. > 0, we have;
At the maximum volume, the width of the block, w = 6. cm ≈ 6.7 cm
The maximum volume, , is therefore given when w = 6.
cm = 20/3 cm as follows;
V = 10·w² - w³
= 10·(20/3)² - (20/3)³ = 4000/27 = 148.
The maximum volume, = 148.
cm³ ≈ 148.1 cm³
Using a graphing calculator, also, we have by finding the extremum of the function V = 10·w² - w³, the coordinate of the maximum point is (20/3, 4000/27)
The width of the box is;
6.7 cm
The maximum volume is;
148.1 cm³
