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

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

Bytelearn · Accepted Answer

Convert to Improper Fractions: step_1: Convert the dimensions of the box from mixed fractions to improper fractions. Width = 3 1/4 inches = 13/4 inches, Length = 4 1/2 inches = 9/2 inches, Height = 2 3/4 inches = 11/4 inches.Calculate Volume: step_2: Calculate the volume of the box using the formula Volume = Width x Length x Height. Volume = (13/4) x (9/2) x (11/4) inches^3.Perform Multiplication: step_3: Perform the multiplication to find the volume. Volume = (13 x 9 x 11) / (4 x 2 x 4) = 1287 / 32 = 40.21875 cubic inches.Calculate Cube Volume: step_4: Calculate the volume of one 1/4 inch cube. Volume of one cube = (1/4) x (1/4) x (1/4) = 1/64 cubic inches.Determine Cube Fit: step_5: Determine how many 1/4 inch cubes fit into the box. Number of cubes = Total volume of box / Volume of one cube = 40.21875 / (1/64) = 2574 cubes.

How many $\frac{1}{4}$ inch cubes does it take to fill a box with width $3\frac{1}{4}$ inches, length $4\frac{1}{2}$ inches, and height $2\frac{3}{4}$ inches? $\newline$ (A) $2$ , $574$ cubes $\newline$ (B) $40$ cubes $\newline$ (C) $644$ cubes $\newline$ (D) $1$ , $536$ cubes

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How many $\frac{1}{4}$ inch cubes does it take to fill a box with width $3\frac{1}{4}$ inches, length $4\frac{1}{2}$ inches, and height $2\frac{3}{4}$ inches? $\newline$ (A) $2$ , $574$ cubes $\newline$ (B) $40$ cubes $\newline$ (C) $644$ cubes $\newline$ (D) $1$ , $536$ cubes