Question

c. choose the one best answer to each question.

1. a slab of concrete will have four concrete blocks in each corner as shown in the drawing below.

if each corner block has the same dimensions, what is the volume of the structure in cubic feet?
a. 72
b. 168
c. 288
d. 360

Explanation:

Step1: Calculate the volume of the large rectangular prism

The formula for the volume of a rectangular prism is \(V = l\times w\times h\). For the large prism, \(l = 12\) ft, \(w=8\) ft, \(h = 3\) ft.

$$V_{large}=12\times8\times3=288$$

Step2: Calculate the volume of one small concrete block

For the small block, \(l = 3\) ft, \(w = 3\) ft, \(h=2\) ft.

$$V_{small}=3\times3\times2 = 18$$

Step3: Calculate the total volume of the four small blocks

Since there are 4 small blocks, \(V_{total - small}=4\times V_{small}\)

$$V_{total - small}=4\times18=72$$

Step4: Calculate the volume of the entire structure

The volume of the structure \(V = V_{large}+V_{total - small}\)

$$V=288 + 72=360$$

Answer:

D. 360