Question

a rectangular box has a height of 7 centimeters and a volume of 336 cubic centimeters. The length of the box is three times the width.

Write an equation describing this situation and find the length and width of the box.

Answer 1

Volume = LxWXH

Volume= 336
Height=7
Width= w
Length=3w

336= 7•w•3w
336=21w^2
16=w^2
W= 4

Width=4 cm
Length=3(4)= 12 cm

Answer 2

The length and width of a box is required.

The equation describing the situation is $V=3W^2H$

Length of the box is 12 cm and width of the box is 4 cm.

h = The height of the box = 7 cm

V = Volume of the box = $336\ \text{cm}^3$

Length of the box is three times the width.

$L=3W$

Volume of a cuboidal box is given by

$V=LWH\\\Rightarrow V=(3W)WH\\\Rightarrow V=3W^2H$

The equation describing the situation is $V=3W^2H$

Solving the equation

$W=\sqrt{\dfrac{V}{3H}}\\\Rightarrow W=\sqrt{\dfrac{336}{3\times 7}}\\\Rightarrow W=\sqrt{16}=4$

$L=3W=3\times 4\\\Rightarrow L=12$

Length of the box is 12 cm and width of the box is 4 cm.

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