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Sergeu [11.5K]
3 years ago
15

Huong packed 189 cubes into small, rectangular, empty box. The cubes cimpletely filled the box. The edge length of each cube was

1/2 of an inch. Which statement correctly finds justifies the box's volume based on the number of cubes packed into it ?
Mathematics
1 answer:
earnstyle [38]3 years ago
3 0

Answer:

See Explanation

Step-by-step explanation:

Given

Cube:

L = \frac{1}{2}\ in

Cubes = 189

The question is incomplete. However, I will solve for the volume of the rectangular box.

First, calculate the volume of 1 cube.

Volume = Length^3

V_1 = L^3

V_1 = \frac{1}{2}^3

V_1 = \frac{1}{8}

The volume of the box is calculated by multiplying the number of cubes by the volume of the cube.

V_2 = 189 * V_1

V_2 = 189 * \frac{1}{8}\ in^3

V_2 = \frac{189}{8}\ in^3

V_2 = 23.625\ in^3

The volume of the box is 23.625\ in^3

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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
Solve 4x^2 - 36x + 32 = 0<br><br>Sorry! It's suppose to be + 32.<br>Please show all work.
mylen [45]

Answer:

x=1, x=8

Step-by-step explanation:

4x2−36x+32=0

Step 1: Factor left side of equation.

4(x−1)(x−8)=0

Step 2: Set factors equal to 0.

x−1=0 or x−8=0

 (+1)        (+8)

x=1 or x=8




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Margarita [4]

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Ron's piano lesson starts in 2 hours. It takes him 30 minutes to get to the lesson. He has
RideAnS [48]

Answer:

2 hours=120 mins

120-(45+25)

120-(70)

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Ron has enough time to finish his homework and walk the dog before his lesson. Ron should overestimate the total time needed. Since Ron has 50 minutes to spare he could add 25 to home work time and another 25 to walking his dog. he still ha time to do both.

4 0
3 years ago
Find p if 45 :72=72 40:p​
leonid [27]
Here

45 :72 = 40:p
Or 45/72=40/p
Or 45p = 72*40

Or p = 2880/45

Or p= 64

Thank you
Ayanas
4 0
3 years ago
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