Question

a terrarium in the shape of a rectangular prism has a volume of 4608 cubic inches. its length is more than 10 inches. the dimensions of the terrarium in terms of width are shown. calculate the length width and height of the terrarium

Answer 1

Answer:

The width is 12 inches, the length is 24 inches, and the height is 16 inches

Step-by-step explanation:

Please see the attached photo, it provides full information we need to solve this problem

We know that:

• volume = 4608 cubic

• Lenth = (36-w)

• With = w

• Hight = w+4

So the vomume fomula is = LWH = (36 -w)*w*(w+4)

<=> $32w^{2}$ + 114w - $-w^{3}$ - 4608

<=> w = 32 and w =  12 and w= -12

Disregard w= -12, because the width cannot be negative, and we also know that length is more than 10 inches so w =  12 is fit with the requirement.

=> Length = 36 -12 = 24

Width = 12 and Hight = 12 + 4 = 16

Answer 2

The length, width, and height of the terrarium that has a shape of a rectangular prism is:

• Length = 24 in
• Width = 12 in.
• Height = 16 in.

What is the Volume of a Rectangular Prism?

Volume of rectangular prism = length × width × height.

Given the dimensions of the terrarium in the shape of a rectangular prism as:

Volume = 4,608 cubic in.

Length = (36 - w) in

Width = w in.

Height = (w + 4) in.

Plug in the values:

4,608 = (36 - w)(w)(w + 4)

4,608 = (36 - w)(w² + 4w)

4,608 = 36(w² + 4w) -w(w² + 4w)

4,608 = 36w² + 144w - w³ - 4w²

36w² + 144w - w³ - 4w² - 4,608 = 0

-w³ + 32w² + 144w - 4,608 = 0

Factorize

w = −12 or w = 12 or w = 32

Since we know the length is more than 10 inches and cannot be negative, therefore, w = 12.

Plug in the value of w

Length = (36 - 12) = 24 in

Width = 12 in.

Height = (12 + 4) = 16 in.

Therefore, the length, width, and height of the terrarium that has a shape of a rectangular prism is:

• Length = 24 in
• Width = 12 in.
• Height = 16 in.

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