Question

A right rectangular prism is packed with cubes of side length fraction 1 over 5 inch. If the prism is packed with 15 cubes along the length, 6 cubes along the width, and 5 cubes along the height, what is the volume of the prism? (1 point) Group of answer choices A. Fraction 2 and 3 over 10 cubic inches B. Fraction 3 and 3 over 5 cubic inches C. Fraction 7 and 1 over 5 cubic inches D. Fraction 7 and 1 over 10 cubic inches

Answer 1

Given:

A right rectangular prism is packed with cubes of side length $\dfrac{1}{5}$ inch.

Prism is packed with 15 cubes along the length, 6 cubes along the width, and 5 cubes along the height.

To find:

The volume of the prism

Solution:

Side length of each cube $=\dfrac{1}{5}$ inch.

15 cubes along the length, so length of prism is

$l=15\times \dfrac{1}{5}=3\text{ inches}$

6 cubes along the width, so width of prism is

$b=6\times \dfrac{1}{5}=\dfrac{6}{5}\text{ inches}$

5 cubes along the height, so height of prism is

$h=5\times \dfrac{1}{5}=1\text{ inch}$

Now,

Volume of rectangular prism is

$V=l\times b\times h$

$V=3\times \dfrac{6}{5}\times 1$

$V=\dfrac{18}{5}$

$V=\dfrac{3\times 5+3}{5}$

$V=3\dfrac{3}{5}\text{ cubic inches}$

Therefore, the correct option is B.