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3 years ago

Alice is constructing rectangular prisms to represent buildings in a diorama for her social

1 answer:

7 0

L = w + 6

w = l - 6

h = w - 5

h = l - 11

V = lwh

V = l(l - 6)(l - 11)

But V <= 50

therefore,

l^3 - 17l^2 + 66l - 50 <= 0

since all the coefficients add to 0, 1 is a root. Therefore, it can be factored into:

(l-1)(l-8+sqrt(14))(l-8-sqrt(14))<= 0

but at the extremes,

h >= 0

l -11 >= 0

l >= 11

therefore, considering this,

we can see that

11 <= l <= 8 + sqrt(14)

11 - 6 <= l - 6 <= 8 + sqrt(14) - 6

5 <= w <= 2 + sqrt(14)

(In cm)

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4 years ago

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(50 POINTS!!!) find the total surface area and volume, then multiply by $0.004. please show your work!!

mrs_skeptik [129]

The Total surface area of the square pyramid = 115.2 in.²

The Volume of the square pyramid = 1,024 in.³.

<h3>What is the Total Surface Area of a Square Pyramid?</h3>

The total surface are of a square pyramid is given as: TSA = SA = 1/2(P × l), where:

P = perimeter of the square base

l = slant height of the pyramid

<h3>What is the Volume of a Square Pyramid?</h3>

The volume of a square pyramid = 1/3(a³ × h), where:

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2 years ago

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3 years ago