Question

a water storage tank is supported by a rectangular prism - shaped concrete pillar, which needs to be coated with a protective sealant to prevent erosion. the entire pillar must be sealed in order to protect the tank. if the pillar is 12 feet tall and has a base that measures 4 feet by 3 feet, what is the total area that needs to be sealed? justify your answer.

Explanation:

Step1: Recall the formula for the surface area of a rectangular prism

The surface area \( SA \) of a rectangular prism is given by the formula \( SA = 2(lw + lh + wh) \), where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
Here, \( l = 4 \) feet, \( w = 3 \) feet, and \( h = 12 \) feet.

Step2: Calculate each term inside the formula

First, calculate \( lw \): \( lw=4\times3 = 12 \) square feet.
Then, calculate \( lh \): \( lh = 4\times12=48 \) square feet.
Next, calculate \( wh \): \( wh=3\times12 = 36 \) square feet.

Step3: Substitute the values into the surface - area formula

Substitute \( lw = 12 \), \( lh = 48 \), and \( wh = 36 \) into the formula \( SA=2(lw + lh+wh) \).
\( SA = 2(12 + 48+36) \)
First, add the values inside the parentheses: \( 12 + 48+36=96 \) square feet.
Then, multiply by 2: \( SA = 2\times96=192 \) square feet.

Answer:

The total area that needs to be sealed is 192 square feet.