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New Tab Mail - Kelvin Jones... Shopping Cart | OP... Building a Better A... What Question 6 of 10 C PREVIOUS QUESTION How many (1)/(4) inch cubes does it take to fill a box with width 3(1)/(4) inches, length 4(1)/(2) inches, and height 2(3)/(4) inches? (A) 2,574 cubes (B) 40 cubes (C) 644 cubes (D) 1,536 cubes

New Tab\newlineMail - Kelvin Jones...\newlineShopping Cart | OP...\newlineBuilding a Better A...\newlineWhat\newlineQuestion 66 of 1010\newlineC PREVIOUS QUESTION\newlineHow many \newline14\frac{1}{4} inch cubes does it take to fill a box with width \newline3143\frac{1}{4} inches, length \newline4124\frac{1}{2} inches, and height \newline2342\frac{3}{4} inches?\newline(A) 22,574574 cubes\newline(B) 4040 cubes\newline(C) 644644 cubes\newline(D) 11,536536 cubes

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Q. New Tab\newlineMail - Kelvin Jones...\newlineShopping Cart | OP...\newlineBuilding a Better A...\newlineWhat\newlineQuestion 66 of 1010\newlineC PREVIOUS QUESTION\newlineHow many \newline14\frac{1}{4} inch cubes does it take to fill a box with width \newline3143\frac{1}{4} inches, length \newline4124\frac{1}{2} inches, and height \newline2342\frac{3}{4} inches?\newline(A) 22,574574 cubes\newline(B) 4040 cubes\newline(C) 644644 cubes\newline(D) 11,536536 cubes
  1. Convert to Improper Fractions: step_1: Convert the dimensions of the box from mixed fractions to improper fractions. Width = 3143 \frac{1}{4} inches = 134\frac{13}{4} inches, Length = 4124 \frac{1}{2} inches = 92\frac{9}{2} inches, Height = 2342 \frac{3}{4} inches = 114\frac{11}{4} inches.
  2. Calculate Volume: step_2: Calculate the volume of the box using the formula Volume=Width×Length×HeightVolume = Width \times Length \times Height. Volume=(134)×(92)×(114)Volume = \left(\frac{13}{4}\right) \times \left(\frac{9}{2}\right) \times \left(\frac{11}{4}\right) inches3^3.
  3. Perform Multiplication: step_3: Perform the multiplication to find the volume. Volume = (13×9×11)/(4×2×4)=1287/32=40.21875(13 \times 9 \times 11) / (4 \times 2 \times 4) = 1287 / 32 = 40.21875 cubic inches.
  4. Calculate Cube Volume: step_4: Calculate the volume of one 14\frac{1}{4} inch cube. Volume of one cube = (14)×(14)×(14)=164\left(\frac{1}{4}\right) \times \left(\frac{1}{4}\right) \times \left(\frac{1}{4}\right) = \frac{1}{64} cubic inches.
  5. Determine Cube Fit: step_5: Determine how many 14\frac{1}{4} inch cubes fit into the box. Number of cubes = Total volume of box / Volume of one cube = 40.21875(164)=2574\frac{40.21875}{\left(\frac{1}{64}\right)} = 2574 cubes.

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