Question

How many cubes with edges 1/4 cm. will fit a rectangular prism with length = 7cm, width = 5 cm and height = 6cm? Show your work.

Answer 1

we can look at this as, hmmm we have a 7x5x6 rectangular prism, whose volume is (7)(5)(6) = 210 cm³. We also have a tiny cube with all sides being ¼, meaning its volume is (¼)(¼)(¼), how many times does that volume go into the larger rectangular prism?

`\stackrel{ \textit{\LARGE volumes} }{\stackrel{ \textit{rectangular prism} }{(7)(5)(6)\implies 210}\hspace{5em}\stackrel{ \textit{tiny cube} }{\left( \cfrac{1}{4} \right)\left( \cfrac{1}{4} \right)\left( \cfrac{1}{4} \right)\implies \cfrac{1}{64}}} \\\\[-0.35em] ~\dotfill\\\\ \textit{how many times does }(1)/(64)\textit{ go into }210?\hspace{2em}\cfrac{210}{~~ ( 1 )/( 64 ) ~~}\implies 210\cdot 64\implies \text{\LARGE 13440}`

Answer 2

here is your answer

Explanation:

To find out how many cubes with edges of 1/4 cm will fit inside a rectangular prism with dimensions of length = 7 cm, width = 5 cm, and height = 6 cm, we need to calculate the volume of the rectangular prism and the volume of the individual cube.

Volume of the rectangular prism:

Volume = length × width × height

Volume = 7 cm × 5 cm × 6 cm

Volume = 210 cm³

Volume of the cube:

Volume = edge length³

Volume = (1/4 cm)³

Volume = 1/64 cm³

To determine how many cubes can fit inside the rectangular prism, we divide the volume of the rectangular prism by the volume of the cube:

Number of cubes = Volume of rectangular prism / Volume of cube

Number of cubes = 210 cm³ / (1/64 cm³)

Dividing by a fraction is equivalent to multiplying by its reciprocal:

Number of cubes = 210 cm³ * (64 cm³/1)

Number of cubes = 13440 cm³

Therefore, the rectangular prism can accommodate 13,440 cubes with edges of 1/4 cm.