Question

Kamila plans to build a concrete block wall behind her house. The wall will be 12 feet long, 6 feet high, and 8 inches thick. Each concrete block measures 16 inches long by 8 inches wide by 8 inches deep. How many blocks will Kamila need to build the wall? Each concrete block has two holes through the middle of the block. The holes are 4 inches wide by 4.5 inches long. What is the volume of one concrete block? Each concrete block weighs 36.5 pounds. What is the total weight of the concrete wall? If each block is solid concrete, how much would one block weigh? In your final answers, include all formulas, equations, and the calculations necessary to determine the correct answers.

Answer 1

This question has a lot of steps. Let's define our goal list:
1) Find the number of blocks
2) Find the volume of one block with two holes
3) Find the weight of the wall
4) Find the weight of one solid block

Starting with question 1. How many blocks does she need?

Well, we know the dimensions of the wall are 144 in (12 ft) x 72 in (6 ft) x 8 in. Since a block is 8 inches deep just like the wall, we'll only need one layer. Each block is 16 inches long, so we'll need 144 ÷ 16 = 9 blocks for the length. Each block is 8 inches high, so we need 72 ÷ 8 = 9 blocks up. 9 blocks high times 9 blocks wide times 1 block deep = 81 blocks for the wall.

Question 2. The volume of one block with two holes.

Let's start with the volume of a solid block. 16 in long x 8 in high x 8 in deep = 1024 in² for the volume. Then we subtract the holes. Each hole is 4 in wide x 4.5 in long x 8 in deep = 144 in², and there are two of them, making 288 in² less volume. 1024 - 288 = 736 in² for the volume of one holey block.

Question 3. The weight of the wall.

Each block is 36.5 lbs. We calculated that we need 81 blocks. So the weight of the wall is 81 x 36.5 = 2956.5 lbs. Heavy wall!

Question 4: The weight of one solid block. 

We know the weight of one block with two holes (which we have calculated the volume as 736 in²) is 36.5 lbs. We also know the volume of a solid block is 1024 in². So 1024 in² × 36.5 lbs/736 in² (dimensional analysis gives us the correct units here) ≈ 50.8 lbs for a solid block.

Does all of this make sense? I know it was a lot. Comment if you need anything else.