Evan is painting a stool that has a cylindrical seat and four rectangular prism legs. The seat has a diameter of 8 inches and a height of 2 inches. Each leg is 2 inches by 2 inches by ten inches. How much area will Evan have to paint? Use three point one four for pi. Show your work.
Area of seat to be painted
= Surface area of cylinder - 4 squares covered by end of legs
= 2π(4^2) + 2π(4)(2) - 4(2^2) = 48π - 16
surface area of legs (assuming he will paint the bottom of the legs):
each leg has 4 surfaces of 2(10) or 20 inches^2
= 4(4)(20) + 4(2)(2)
= 336
total area = 48π-16+336
= 470.72
check my arithmetic
You should allow them to do their own test! You should not do it for them!
To find the total area that Evan will have to paint, we need to calculate the surface area of the cylindrical seat and the surface area of the four rectangular prism legs.
First, let's calculate the surface area of the cylindrical seat. The formula for the surface area of a cylinder is given by:
Area = 2πr * h + πr²,
where r is the radius and h is the height.
Given that the diameter of the seat is 8 inches, we can find the radius by dividing the diameter by 2:
Radius = 8 inches / 2 = 4 inches.
Using the given value of pi as 3.14, we can calculate the surface area of the cylindrical seat as follows:
Area_seat = 2 * 3.14 * 4 inches * 2 inches + 3.14 * (4 inches)²
= 25.12 inches² + 50.24 inches²
= 75.36 inches².
Next, let's calculate the surface area of the four rectangular prism legs. The formula for the surface area of a rectangular prism is given by:
Area = 2lw + 2lh + 2wh,
where l is the length, w is the width, and h is the height.
Given that each leg has dimensions of 2 inches by 2 inches by 10 inches, we can calculate the surface area of one leg as follows:
Area_leg = 2 * 2 inches * 2 inches + 2 * 2 inches * 10 inches + 2 * 2 inches * 10 inches
= 8 inches² + 40 inches² + 40 inches²
= 88 inches².
Since there are four legs, the total surface area of the legs will be:
Total_leg_area = 4 * Area_leg
= 4 * 88 inches²
= 352 inches².
Finally, to find the total area Evan will have to paint, we add the surface area of the seat and the surface area of the legs together:
Total_area = Area_seat + Total_leg_area
= 75.36 inches² + 352 inches²
= 427.36 inches².
Therefore, Evan will have to paint approximately 427.36 square inches.