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Vesna [10]
3 years ago
15

A rectangular pyramid is sliced such that the cross section is perpendicular to its base and the cross section does not intersec

t its vertex.
What is the shape of the cross section?


square

trapezoid

triangle

rectangle
Mathematics
2 answers:
EleoNora [17]3 years ago
5 0

Answer:

im pretty sure the answer is TRAPEZOID.

Step-by-step explanation:

o-na [289]3 years ago
5 0

The vertex, would be the tip of the pyramid. If it was sliced at the vertex, the shape would be a triangle. Since the slice doesn't intersect the vertex, the point of the pyramid would net be included, it would be as if the tip was cut off.

You would then have a trapezoid, because the top would be a straight horizontal line parallel with the bottom line.

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solong [7]

Answer:

The volume is increasing at a rate of 16286 in³/min.

Step-by-step explanation:

a) The volume of a cone is given by:

V = \frac{1}{3}h\pi r^{2}

Where:    

r: is the radius

h: is the height

The rate of change of the volume can be calculated by using the chain rule:

\frac{dV}{dt} = \frac{\pi}{3}[\frac{dh}{dt}r^{2} + h\frac{d(r^{2})}{dt}]

Since h = 4/3 r we have:

\frac{dV}{dt} = \frac{\pi}{3}[\frac{d(\frac{4r}{3})}{dt}r^{2} + \frac{4r}{3}\frac{d(r^{2})}{dt}]

\frac{dV}{dt} = \frac{4\pi}{9}[\frac{dr}{dt}r^{2} + r\frac{d(r^{2})}{dt}]        

\frac{dV}{dt} = \frac{4\pi}{9}[\frac{dr}{dt}r^{2} + 2r^{2}\frac{dr}{dt}]    (1)    

With:

\frac{dr}{dt} = 3 in/min

r = 3 ft*\frac{12 in}{1 ft} = 36 in

And by entering the above values into equation (1) we have:

\frac{dV}{dt} = \frac{4\pi}{9}[(3 in/min)*(36 in)^{2} + 2*(36 in)^{2}*3 in/min]

\frac{dV}{dt} = 16286 in^{3}/min

Therefore, the volume is increasing at a rate of 16286 in³/min.

I hope it helps you!                                    

3 0
3 years ago
According to the diagram below, In which hemisphere is it DAY and WINTER?
Vanyuwa [196]
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2 years ago
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valina [46]

Answer:

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6 0
3 years ago
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Nina [5.8K]

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x^{3} -15x^{2} + 75x-125

Step-by-step explanation:

6 0
2 years ago
4.
kow [346]

Answer:

B

Step-by-step explanation:

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