Question

The height of a rectangular prism is half its width The width of the prism is 1/3 of its length If the width of the prism is 3 centimeters, what is the volume?

Answer 1

Answer:

40.5 centimeters.

Step-by-step explanation:

Given:

The width of the prism is 3 centimeters.

The width of the prism is 1/3 of its length.

The height of a rectangular prism is half its width.

To find:

Volume of a rectangular prism = ?

Solution:

Width of the prism = 3 cm

As given, height of a rectangular prism is half its width.

height of a rectangular prism = $\frac{1}{2} \times3=\frac{3}{2} \ cm$

Similarly, as given, the width of the prism is 1/3 of its length.

Width of the prism = $\frac{1}{3}\ of\ length$

                            $3=\frac{1}{3}\times length$

By multiplying both sides by 3

                            $3\times3=\frac{1}{3} \times3\ length\\9= length$

Thus, length of prism = 9 cm

Now, as we know:

$Volume\ of\ rectangular\ prism=length\times breadth\times height$

                                                 $=9\times3\times\frac{3}{2} \\\\ =\frac{81}{2} \\ \\ =40.5\ cm$

Therefore, the volume of a rectangular prism is 40.5 centimeters.