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Elan Coil [88]
3 years ago
11

Pyramid A is a right square pyramid with a height of 100 m and a square base with a perimeter of 356 m. Pyramid B has a square b

ase with a perimeter of 456 m and a height of 215 m. Which pyramid has the greater volume and by how many times as​ great? g
Mathematics
1 answer:
Tomtit [17]3 years ago
3 0

Answer:

The volume of pyramid B is 3.5 times greater than the volume of pyramid A

Step-by-step explanation:

The area of squared based a pyramid is given by:

Area = \frac{1}{3}*s*s*h

Where 's' the length of the side of the base and 'h' is the height.

For pyramid A:

h= 100 m

s= 356/4 = 89 m

Area_A = \frac{1}{3}*89*89*100\\Area_A=264,033.33\ m^3

For pyramid B:

h= 215 m

s= 456/4 = 114 m

Area_B = \frac{1}{3}*114*114*215\\Area_B=931,380\ m^3

Pyramid B has a greater volume and the ratio between volumes is:

\frac{Area_B}{Area_A} =\frac{931,380}{264,033.33}\\\frac{Area_B}{Area_A} =3.5

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Answer:

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Step-by-step explanation:

1. The selection of answers offers a choice of positive or negative slope, a slope of about 4 or about 35, and y-intercepts from the same set of values.

If you consider a couple of points (at the ends of the domain is usually a good choice), you see the slope is about 4 and the y-intercept is around 30.

For example, the points (5, 50) and (15, 91) have a slope of (91-50)/(15-5) = 4.1 so will give rise to the equation ...

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Filling in x=0 gives y = 50 -20.5 = 29.5

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2. If we look at a few other data points, we see that they have a generally upward trend that matches the above equation pretty well. That suggests a very high value of correlation, so the appropriate choices would be 0.93 or 0.96. Of course, the correlation is positive, matching the sign of the slope of the regression line. (Since the data points do not fall exactly on a line, the correlation is not 1.00. My assessment is they fall close enough to the line to rate a correlation of .96 instead of .93.)

At this point, the output of your calculator can confirm that the correlation coefficient is closer to 0.96. Mine says r = 0.9624.

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3. We have already determined by examining the data points that the correlation is "very strong." The correlation coefficient of 0.96 confirms this.

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4. Using the equation of part 1, we can find the number of study hours:

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