A cylindrical flower pot with an open top needs to be painted. The height of the pot is 9 inches and the radius is 3 inches. If it takes Troy 5 minutes to paint 40 square inches, how long to the minute will it take him to paint the outside of the flower pot?
I came up with 20 minutes
Area of the curved surface ("outside") is
A = 2πrh
where r=3", h=9".
Check your arithmetic, I came up with a little more than 20 minutes.
To find the time it takes for Troy to paint the outside of the flower pot, we need to calculate the surface area of the pot and divide it by Troy's painting rate.
First, let's calculate the lateral surface area of the cylindrical flower pot. The lateral surface area is the surface area excluding the top and bottom.
The formula to calculate the lateral surface area of a cylinder is:
Lateral Surface Area = 2 * π * radius * height
Given the radius is 3 inches and the height is 9 inches, we can substitute these values into the formula:
Lateral Surface Area = 2 * π * 3 * 9
Next, we can simplify and calculate the value:
Lateral Surface Area = 54π square inches
Now, we divide the lateral surface area by Troy's painting rate of 40 square inches per 5 minutes:
Time for Troy to paint the outside of the flower pot = (Lateral Surface Area) / (Painting Rate)
Time for Troy to paint the outside of the flower pot = (54π) / 40 * 5
Using a calculator, we can simplify this further:
Time for Troy to paint the outside of the flower pot ≈ 12.78 minutes
So, it will take approximately 12.78 minutes for Troy to paint the outside of the flower pot.