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A large concrete block is used for the cornerstone of a building. The block is [tex]13 \, \text{ft}[/tex] deep, [tex]11 \, \text{ft}[/tex] wide, and [tex]16 \, \text{ft}[/tex] long. What volume of concrete is needed to make this block?

A. [tex]2288 \, \text{ft}^3[/tex]
B. [tex]40 \, \text{ft}^3[/tex]
C. [tex]159 \, \text{ft}^3[/tex]
D. [tex]189 \, \text{ft}^3[/tex]


Sagot :

Sure! Let's determine the volume of the concrete block using the provided dimensions.

To find the volume of a rectangular prism (in this case, a concrete block), we use the formula:

[tex]\[ \text{Volume} = \text{depth} \times \text{width} \times \text{length} \][/tex]

Given the dimensions:
- Depth = 13 feet
- Width = 11 feet
- Length = 16 feet

We can substitute these values into the formula to get the volume:

[tex]\[ \text{Volume} = 13 \, \text{ft} \times 11 \, \text{ft} \times 16 \, \text{ft} \][/tex]

Let's do the multiplication step by step:

1. First, multiply the depth by the width:
[tex]\[ 13 \, \text{ft} \times 11 \, \text{ft} = 143 \, \text{ft}^2 \][/tex]

2. Next, multiply the result by the length:
[tex]\[ 143 \, \text{ft}^2 \times 16 \, \text{ft} = 2288 \, \text{ft}^3 \][/tex]

So, the volume of the concrete block is:

[tex]\[ 2288 \, \text{ft}^3 \][/tex]

Therefore, the correct answer from the given options is:

[tex]\[ 2288 \, \text{ft}^3 \][/tex]