A rectangular bin 4 feet long, 3 feet wide, and 2 feet high is solidly packed with bricks whose dimensions are 8 inches, 4 inches, and 2 inches. The number of bricks in the bin is
A. 54
B. 648
C. 1298
D. NONE
volume of box = 4*3*2 = 24 ft^3
volume of brick = 8/12 *4/12 * 2/12
= 2/3 * 1/3 *1/6 = 1/3 * 1/3 *1/3
= 1/27 ft^3
24/ (1/27) = 648
D. NONE
Because the dimensions of the bin are given in feet, while the dimensions of the bricks are given in inches, we need to convert the dimensions of the bin to inches in order to make a proper comparison.
The dimensions of the bin in inches are:
Length: 4 feet = 48 inches
Width: 3 feet = 36 inches
Height: 2 feet = 24 inches
Now, let's calculate the number of bricks that can fit in the bin.
Volume of the bin = Length x Width x Height
Volume of the bin = 48 inches x 36 inches x 24 inches
Volume of a brick = Length x Width x Height
Volume of a brick = 8 inches x 4 inches x 2 inches
Number of bricks = Volume of the bin / Volume of a brick
Number of bricks = (48 inches x 36 inches x 24 inches) / (8 inches x 4 inches x 2 inches)
After simplification, the units of inches cancel out, and we get:
Number of bricks = (48 x 36 x 24) / (8 x 4 x 2)
Number of bricks = 36 x 12
Number of bricks = 432
Therefore, none of the given answer choices is correct. The correct answer should be 432.
To find the number of bricks in the bin, we need to determine how many bricks can fit in each dimension.
The dimensions of the bin are given in feet, so we need to convert the dimensions of the bricks to feet:
8 inches = 8/12 = 2/3 feet
4 inches = 4/12 = 1/3 feet
2 inches = 2/12 = 1/6 feet
Next, we need to find the number of bricks that can fit in each dimension:
Length of the bin = 4 feet
Length of a brick = 2/3 feet
Number of bricks in the length dimension = (4 feet) / (2/3 feet) = (4 feet) * (3/2) = 6 bricks
Width of the bin = 3 feet
Width of a brick = 1/3 feet
Number of bricks in the width dimension = (3 feet) / (1/3 feet) = (3 feet) * (3/1) = 9 bricks
Height of the bin = 2 feet
Height of a brick = 1/6 feet
Number of bricks in the height dimension = (2 feet) / (1/6 feet) = (2 feet) * (6/1) = 12 bricks
To find the total number of bricks, we multiply the number of bricks in each dimension:
Total number of bricks = (Number of bricks in the length dimension) * (Number of bricks in the width dimension) * (Number of bricks in the height dimension)
Total number of bricks = 6 * 9 * 12 = 648
Therefore, the number of bricks in the bin is 648.
The answer is B. 648.
To find the number of bricks in the bin, we need to determine the volume of the bin as well as the volume of each brick. Then, we can divide the volume of the bin by the volume of each brick to get the total number of bricks.
First, let's calculate the volume of the bin. The volume of a rectangular shape can be found by multiplying its length, width, and height.
Given:
Length of bin = 4 feet = 48 inches
Width of bin = 3 feet = 36 inches
Height of bin = 2 feet = 24 inches
Volume of bin = Length × Width × Height
= 48 inches × 36 inches × 24 inches
Now, let's calculate the volume of each brick. The volume of a rectangular solid can be found by multiplying its length, width, and height.
Given:
Length of brick = 8 inches
Width of brick = 4 inches
Height of brick = 2 inches
Volume of brick = Length × Width × Height
= 8 inches × 4 inches × 2 inches
Next, we need to divide the volume of the bin by the volume of each brick to get the total number of bricks.
Total number of bricks = Volume of bin / Volume of each brick
= (48 inches × 36 inches × 24 inches) / (8 inches × 4 inches × 2 inches)
Now, let's simplify and calculate the resulting value:
Total number of bricks = (48 × 36 × 24) / (8 × 4 × 2)
= 497664 / 64
= 7776
Therefore, the number of bricks in the bin is 7776.
The correct answer choice is not provided, so the answer could be D. NONE.