Question

How many cubes with side lengths of \dfrac13\text{ cm} 3 1 ​ cmstart fraction, 1, divided by, 3, end fraction, start text, space, c, m, end text does it take to fill the prism?

Answer 1

How many cubes with side lengths of \dfrac13\text{ cm} 3 1 ​ cmstart fraction, 1, divided by, 3, end fraction, start text, space, c, m, end text does it take to fill the prism?

The correct question is,

How many cubes with side lengths of 1/3 cm needed to fill the prism of volume 3 cubic units?

Given,

Volume of prism = 3 cubic units

Side lengths of cube = 1/3

Therefore the volume of the cube is,

V = a³   (a = side of the cube)

V = 1/3 × 1/3 × 1/3

= ( 1/3 )³  

= 1/27 cubic units

= 0.037037037 cubic units

In order to find the number of cubes needed to fill the prism, we need to divide the volume of cube by volume of the prism.

Therefore, we get,

= Volume of prism / Volume of cube

= 3 / 0.037037037

= 81

Therefore, 81 cubes are needed to fill the prism.

Answer 2

★ Correct question :

How many cubes with side lengths of 1/3 cm needed to fill the prism of volume 3 cubic units?

$\rule{200}{1}$

☯ Given :

Volume of prism = 3 unit³

Side lengths of cube = 1/3

$\rule{200}{1}$

☯ Solution :

We know that,

$\Large{\implies{\boxed{\boxed{\sf{Volume = a^3}}}}}$

Where,

• a is the side of the cube

$\sf{\dashrightarrow Volume = \bigg(\dfrac{1}{3}\bigg)^3} \\ \\ \sf{\dashrightarrow Volume = \frac{1}{27}} \\ \\ \sf{\dashrightarrow Volume = 0.0370370} \\ \\ \Large{\implies{\boxed{\boxed{\sf{Volume = 0.0370370 \: unit^3}}}}}$

$\rule{200}{2}$

Now,

As, we have to find the number if cubes so we will devide volume of prism by volume of one cube

$\small{\sf{\dashrightarrow No. \: of \: cubes = \dfrac{Volume \: of \: prism} {Volume \: of \: cube}}} \\ \\ \small{\sf{\dashrightarrow No. \: of \: cubes = \dfrac{3}{0.0370370}}} \\ \\ \small{\sf{\dashrightarrow No. \: of \: cubes = 81}}$

$\small{\implies{\boxed{\boxed{\sf{No. \: of \: cubes = 81}}}}}$