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FinnZ [79.3K]
3 years ago
14

An open, rectangular box with length of 6 feet, width of 4 feet, and height of 2.5 feet is to be painted on all exterior sides,

including the bottom, with a special waterproof coating. Each gallon of this special coating covers 12 square feet of surface area and costs $36.00. The box is then to be filled with water that weighs approximately 62 pounds per cubic foot.
Mathematics
1 answer:
Sonja [21]3 years ago
8 0

Complete Question

An open rectangular box with length of 6 feet, width of 4 feet and height of 2.5 feet is to be painted on all exterior sides, including the bottom, with a special waterproof coating. Each gallon of this special coating covers 12 square feet of surface area and costs $36.00. The box is then to be filled with water that weighs approximately 62 pounds per cubic foot.

A. Find the cost of painting this open box.

B. Find the weight of the water in the filled box

Answer:

A

x = \$ 294

B

z =  3720 \  pounds

Step-by-step explanation:

From the question we are told that  

  The length is  l  =  6 \ ft

    The width is  b =  4 \ ft

   The height is h  =  2.5 \  ft

Generally the total surface area of the open, rectangular box is mathematically represented as

       T_ A = 2lb + 2lh + 2bh

=>   T_ A = 2(6 * 4) + 2(6 * 2.5) + 2(4 * 2.5)  

=>   T_ A = 98 \ ft^2

From the question we are told that

     $36.00 worth of paint  covers  12 ft^2

So  $x worth of paint covers  98 \ ft^2

=>  x = \frac{98 * 36}{12}

=>   x = \$ 294

Generally the volume of the open, rectangular box is mathematically represented as

     V  =  l *  b  *  h

=>   V  =  6 *  4  *  2.5

=>   V  =  60 \ ft^3

From the question we are told that  

1 ft^3  weigh 62 pounds

60 \ ft^3 weigh z pounds

=>  z = \frac{60 * 62}{1}

=> z =  3720 \  pounds

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