Question

Gabriel bought a rectangular prism of volume 1296 cu cm. He noticed that in the prism, the length was thrice the height, while the width was twice the height. Help him to find the length, width, and height of the prism.

Answer 1

It is given that the length is thrice the height of the rectangular prism.

Let x cm be the height.

Length = 3 × x = 3x cm

The width is twice the height of the rectangular prism.

Width = 2 × x = 2x cm

The volume of the prism

= Length × Width × Height

= x × 2x × 3x

$=6x^3\text{cu cm}$

$\text{Hence, the volume of the prism is}6x^3\text{cu cm.}$

Given volume of the prism = 1296 cu cm

So, we get:

$6x^3=1296$

$\Rightarrow x^3=\frac{1296}{6}=216$

$\Rightarrow x=\sqrt[3]{3216}=\text{6 cm}$

So, height of the prism = 6 cm

Width of the prism = 2 × x = 2 × 6 = 12 cm

Length of the prism = 3 × x = 3 × 6 = 18 cm

Hence, width = 12cm, heigtht = 6 cm, and length = 18 cm

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