Solved on Jan 12, 2024

Determine how many rectangular prism-shaped concrete bricks a company made given the brick dimensions and total concrete volume used.
$13 \text{ in} \times 5 \text{ in} \times 4 \text{ in}$ brick dimensions, $11,700 \mathrm{in}^{3}$ concrete volume.

STEP 1

Assumptions
1. Each brick is shaped like a rectangular prism.
2. The dimensions of each brick are 13 inches in length, 5 inches in width, and 4 inches in height.
3. The total volume of concrete used is $11,700 \mathrm{in}^{3}$ .
4. The volume of concrete used to make each brick is the volume of the brick itself.

STEP 2

First, we need to calculate the volume of a single brick. The volume $V$ of a rectangular prism is given by the formula:
$V = \text{length} \times \text{width} \times \text{height}$

STEP 3

Now, plug in the given dimensions for the length, width, and height to calculate the volume of a single brick.
$V = 13 \text{ inches} \times 5 \text{ inches} \times 4 \text{ inches}$

STEP 4

Calculate the volume of a single brick.
$V = 13 \times 5 \times 4 = 260 \mathrm{in}^{3}$

STEP 5

Now that we have the volume of a single brick, we can find out how many bricks were made by dividing the total volume of concrete used by the volume of a single brick.
$\text{Number of bricks} = \frac{\text{Total volume of concrete used}}{\text{Volume of a single brick}}$

STEP 6

Plug in the values for the total volume of concrete used and the volume of a single brick to calculate the number of bricks.
$\text{Number of bricks} = \frac{11,700 \mathrm{in}^{3}}{260 \mathrm{in}^{3}}$

STEP 7

Calculate the number of bricks made.
$\text{Number of bricks} = \frac{11,700}{260} = 45$
The company made 45 bricks.

Was this helpful?

Determine how many rectangular prism-shaped concrete bricks a company made given the brick dimensions and total concrete volume used.
$13 \text{ in} \times 5 \text{ in} \times 4 \text{ in}$ brick dimensions, $11,700 \mathrm{in}^{3}$ concrete volume.

STEP 1

STEP 2

First, we need to calculate the volume of a single brick. The volume $V$ of a rectangular prism is given by the formula:
$V = \text{length} \times \text{width} \times \text{height}$

STEP 3

Now, plug in the given dimensions for the length, width, and height to calculate the volume of a single brick.
$V = 13 \text{ inches} \times 5 \text{ inches} \times 4 \text{ inches}$

STEP 4

Calculate the volume of a single brick.
$V = 13 \times 5 \times 4 = 260 \mathrm{in}^{3}$

STEP 5

Now that we have the volume of a single brick, we can find out how many bricks were made by dividing the total volume of concrete used by the volume of a single brick.
$\text{Number of bricks} = \frac{\text{Total volume of concrete used}}{\text{Volume of a single brick}}$

STEP 6

Plug in the values for the total volume of concrete used and the volume of a single brick to calculate the number of bricks.
$\text{Number of bricks} = \frac{11,700 \mathrm{in}^{3}}{260 \mathrm{in}^{3}}$

STEP 7

Calculate the number of bricks made.
$\text{Number of bricks} = \frac{11,700}{260} = 45$
The company made 45 bricks.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Determine how many rectangular prism-shaped concrete bricks a company made given the brick dimensions and total concrete volume used.13 in×5 in×4 in13 \text{ in} \times 5 \text{ in} \times 4 \text{ in}13 in×5 in×4 in brick dimensions, 11,700in311,700 \mathrm{in}^{3}11,700in3 concrete volume.

STEP 1

STEP 2

First, we need to calculate the volume of a single brick. The volume VVV of a rectangular prism is given by the formula:V=length×width×heightV = \text{length} \times \text{width} \times \text{height}V=length×width×height

STEP 3

Now, plug in the given dimensions for the length, width, and height to calculate the volume of a single brick.V=13 inches×5 inches×4 inchesV = 13 \text{ inches} \times 5 \text{ inches} \times 4 \text{ inches}V=13 inches×5 inches×4 inches

STEP 4

Calculate the volume of a single brick.V=13×5×4=260in3V = 13 \times 5 \times 4 = 260 \mathrm{in}^{3}V=13×5×4=260in3

STEP 5

STEP 6

Plug in the values for the total volume of concrete used and the volume of a single brick to calculate the number of bricks.Number of bricks=11,700in3260in3\text{Number of bricks} = \frac{11,700 \mathrm{in}^{3}}{260 \mathrm{in}^{3}}Number of bricks=260in311,700in3​

STEP 7

Calculate the number of bricks made.Number of bricks=11,700260=45\text{Number of bricks} = \frac{11,700}{260} = 45Number of bricks=26011,700​=45The company made 45 bricks.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Determine how many rectangular prism-shaped concrete bricks a company made given the brick dimensions and total concrete volume used.
$13 \text{ in} \times 5 \text{ in} \times 4 \text{ in}$ brick dimensions, $11,700 \mathrm{in}^{3}$ concrete volume.

First, we need to calculate the volume of a single brick. The volume $V$ of a rectangular prism is given by the formula:
$V = \text{length} \times \text{width} \times \text{height}$

Now, plug in the given dimensions for the length, width, and height to calculate the volume of a single brick.
$V = 13 \text{ inches} \times 5 \text{ inches} \times 4 \text{ inches}$

Calculate the volume of a single brick.
$V = 13 \times 5 \times 4 = 260 \mathrm{in}^{3}$

Plug in the values for the total volume of concrete used and the volume of a single brick to calculate the number of bricks.
$\text{Number of bricks} = \frac{11,700 \mathrm{in}^{3}}{260 \mathrm{in}^{3}}$

Calculate the number of bricks made.
$\text{Number of bricks} = \frac{11,700}{260} = 45$
The company made 45 bricks.