Question

geometry the volume of the rectangular prism at the right is 440 cubic centimeters what is the width

Answer 1

The width of the rectangular prism that has a volume of 440 cubic centimeters as shown in the image is: 5 cm

Recall;

Volume of rectangular prism is: $V = length \times width \times height$

From the image given, the dimension of the rectangular prism are:

• l = x
• w = x - 3
• h = x + 3
• Volume = 440

Plug in the values into the volume formula:

$x(x-3)(x+3) = 440$

Find the value of x

$x(x^2 - 9) = 440\\\\x^3 - 9x = 440\\\\x^3 - 9x - 440 = 0$

Factorize

$(x - 8)(x^2 + 8x + 55) = 0$

We can determine the value of x using one of the factors that will give us a positive value.

Thus:

x - 8 = 0

x = 0 + 8

x = 8

• Find the width

width(w) = x - 3

• Plug in the value of x

width (w) = 8 - 3

width (w) = 5 cm

Therefore, the width of the rectangular prism as shown in the image is: 5 cm

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