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A rectangular block has a length of 8 inches, a width of 3.5 inches, and a height of 2 inches.

Six blocks are stacked to create a tower. What is the volume of the tower?

A. [tex]$56 \, \text{in}^3$[/tex]
B. [tex]$336 \, \text{in}^3$[/tex]
C. [tex]$168 \, \text{in}^3$[/tex]
D. [tex]$280 \, \text{in}^3$[/tex]


Sagot :

To determine the volume of the tower created by stacking six rectangular blocks, we need to follow a series of steps.

First, we calculate the volume of one rectangular block. The formula for the volume [tex]\( V \)[/tex] of a rectangular prism is given by:
[tex]\[ V = \text{length} \times \text{width} \times \text{height} \][/tex]

Given the dimensions of one block:
- Length = 8 inches
- Width = 3.5 inches
- Height = 2 inches

Now, we plug these values into the formula:
[tex]\[ V = 8 \times 3.5 \times 2 \][/tex]

Calculating the volume of one block:
[tex]\[ 8 \times 3.5 = 28 \][/tex]
[tex]\[ 28 \times 2 = 56 \][/tex]

So, the volume of one block is 56 cubic inches.

Next, since there are six such blocks stacked to create a tower, we need to find the total volume of the six blocks combined. We can do this by multiplying the volume of one block by the number of blocks:
[tex]\[ \text{Volume of the tower} = \text{Volume of one block} \times \text{Number of blocks} \][/tex]

Plugging in the values we have:
[tex]\[ \text{Volume of the tower} = 56 \times 6 \][/tex]

Calculating:
[tex]\[ 56 \times 6 = 336 \][/tex]

Thus, the volume of the tower is 336 cubic inches.

Therefore, the correct answer is:
[tex]\[ B. 336 \text{ in}^3 \][/tex]
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