Answer :
To determine how many cans of paint are needed to paint the walls of a circular room with a given diameter and height, and given the coverage of a single can, let's go through the calculations step-by-step.
1. Find the circumference of the circular room.
The circumference [tex]\(C\)[/tex] of a circle can be calculated using the formula:
[tex]\[ C = \pi \times \text{diameter} \][/tex]
Given the diameter is 20 feet:
[tex]\[ C = \pi \times 20 \approx 62.8319 \text{ feet} \][/tex]
2. Calculate the area of the walls.
The walls form a cylindrical shape with the circumference being the width and the height being the height of the cylinder. The surface area [tex]\(A\)[/tex] of the walls is then:
[tex]\[ A = \text{circumference} \times \text{height} \][/tex]
Given the height is 9 feet:
[tex]\[ A = 62.8319 \times 9 \approx 565.4867 \text{ square feet} \][/tex]
3. Determine the number of cans of paint needed.
Each can of paint covers an area of 150 square feet. To find out how many cans are needed, divide the total wall area by the coverage of one can and round up to the next whole number, because you can't purchase a fraction of a can.
[tex]\[ \text{Number of cans} = \left\lceil \frac{A}{\text{paint coverage}} \right\rceil \][/tex]
Where:
[tex]\[ \text{paint coverage} = 150 \text{ square feet per can} \][/tex]
Calculate:
[tex]\[ \text{Number of cans} = \left\lceil \frac{565.4867}{150} \right\rceil \approx \left\lceil 3.77 \right\rceil = 4 \][/tex]
Therefore, you will need to buy 4 cans of paint to paint the walls of the circular room.
1. Find the circumference of the circular room.
The circumference [tex]\(C\)[/tex] of a circle can be calculated using the formula:
[tex]\[ C = \pi \times \text{diameter} \][/tex]
Given the diameter is 20 feet:
[tex]\[ C = \pi \times 20 \approx 62.8319 \text{ feet} \][/tex]
2. Calculate the area of the walls.
The walls form a cylindrical shape with the circumference being the width and the height being the height of the cylinder. The surface area [tex]\(A\)[/tex] of the walls is then:
[tex]\[ A = \text{circumference} \times \text{height} \][/tex]
Given the height is 9 feet:
[tex]\[ A = 62.8319 \times 9 \approx 565.4867 \text{ square feet} \][/tex]
3. Determine the number of cans of paint needed.
Each can of paint covers an area of 150 square feet. To find out how many cans are needed, divide the total wall area by the coverage of one can and round up to the next whole number, because you can't purchase a fraction of a can.
[tex]\[ \text{Number of cans} = \left\lceil \frac{A}{\text{paint coverage}} \right\rceil \][/tex]
Where:
[tex]\[ \text{paint coverage} = 150 \text{ square feet per can} \][/tex]
Calculate:
[tex]\[ \text{Number of cans} = \left\lceil \frac{565.4867}{150} \right\rceil \approx \left\lceil 3.77 \right\rceil = 4 \][/tex]
Therefore, you will need to buy 4 cans of paint to paint the walls of the circular room.
