Can Somebody Solve This Inequality? Show Work

Alexxandr [17]

The answer is B
Deductive reasoning

8 0

2 years ago

small cubes with edge lengths of 1/4 inch will be packed into the right rectangular prism shown.( the base is 4 1/2, the width i

ss7ja [257]

General Idea:

We need to find the volume of the small cube given the side length of the small cube as 1/4 inch.

Also we need to find the volume of the right rectangular prism with the given dimension (the height is 4 1/2, the width is 5, and the length is 3 3/4).

To find the number of small cubes that are needed to completely fill the right rectangular prism, we need to divide volume of right rectangular prism by volume of each small cube.

Formula Used:

$Volume \; of \; Cube = a^3 \; \\\{where \; a \; is \; side \; length \; of \; cube\}\\\\Volume \; of \; Right \; Rectangular \; Prism=L \times W \times H\\\{Where \; L \; is \; Length, \; W \; is \; Width, \;and \; H \; is \; Height\}$

Applying the concept:

Volume of Small Cube:

$V_{cube}= (\frac{1}{4} )^3= \frac{1}{64} \; in^3\\\\V_{Prism}= 3 \frac{3}{4} \times 5 \times 4 \frac{1}{2} = \frac{15}{4} \times \frac{5}{1} \times \frac{9}{2} = \frac{675}{8} \\\\Number \; of \; small \; cubes= \frac{V_{Prism}}{V_{Cube}} = \frac{675}{8} \div \frac{1}{64} \\\\Flip \; the \; second \; fraction\; and \; multiply \; with \; the \; first \; fraction\\\\Number \; of \; small \; cubes \;= \frac{675}{8} \times \frac{64}{1} = 5400$

Conclusion:

The number of small cubes with side length as 1/4 inches that are needed to completely fill the right rectangular prism whose height is 4 1/2 inches, width is 5 inches, and length is 3 3/4 inches is <em><u>5400 </u></em>

4 0

3 years ago

Read 2 more answers

Only answer if you actually want to help me please

mamaluj [8]

the answer is circle idk if it's right but it could be I'm in high school I've been through algebra 1 now in geometry