Question

A building is constructed using bricks that can be modeled as right rectangular prisms with a dimension of 8 1/4 x 2 1/4 x 3 1/2. If the bricks cost $0.02 per cubic inch, find the cost of 2000 bricks. Round your answer to the nearest cent

Answer 1

GIVEN:

We are told that a right rectangular brick has the following dimensions;

`8(1)/(4)in*2(1)/(4)in*3(1)/(2)in`

Also, each brick costs $0.02 per cubic inch.

Required;

To find the cost of 2,000 bricks.

Step-by-step solution;

We know the cost per cubic inch, and therefore we will need to find the cost for the total cubic inches per brick. We begin by calculating the volume of each brick as shown below;

`\begin{gathered} Volume\text{ }of\text{ }rectangular\text{ }prism: \\ \\ Volume=l* w* h \end{gathered}`

Therefore,

`\begin{gathered} Volume=8(1)/(4)*2(1)/(4)*3(1)/(2) \\ \\ Volume=(33)/(4)*(9)/(4)*(7)/(2) \\ \\ Volume=(2079)/(32)in^3 \end{gathered}`

Next step, we multiply the volume of one brick by the cost per cubic inches. This is shown below;

`\begin{gathered} Cost\text{ }of\text{ }1\text{ }brick=Cost\text{ }per\text{ }cubic\text{ }inch* volume \\ \\ Cost\text{ }of\text{ }1\text{ }brick=0.02*(2079)/(32) \\ \\ Cost\text{ }of\text{ }1\text{ }brick=1.299375 \end{gathered}`

We now have the cost of 1 brick calculated as $1.299375.

We can now calculate the cost of 2000 bricks as follows;

`\begin{gathered} Cost\text{ }of\text{ }1\text{ }brick=1.299375 \\ \\ Cost\text{ }of\text{ }2000\text{ }bricks=2000*1.299375 \\ \\ Cost\text{ }of\text{ }2000\text{ }bricks=2598.75 \\ \\ Rounded\text{ }to\text{ }the\text{ }nearest\text{ }cent: \\ \\ Cost\text{ }of\text{ }2000\text{ }bricks=2598.80 \end{gathered}`

ANSWER:

The cost of 2,000 bricks will be $2,598.80