Question 19 options:
Solve the problem.
A cylindrical gasoline storage tank on Mr. Edwards' farm needs to be painted. The tank is 8 feet long and has a diameter of 4 feet. If one gallon of paint covers 350 square feet, how many cans of paint will Mr. Edwards need? Use straight pi = 3.14.
Blank Space__________can(s)
To find the surface area of the cylindrical tank, we first need to find the area of the top and bottom circles of the tank, and then the area of the curved surface.
The area of a circle is found using the formula A = πr^2, where r is the radius of the circle.
Given that the diameter of the tank is 4 feet, the radius is 4/2 = 2 feet.
The top and bottom circles have the same radius, so the area of each circle is:
A_circle = π(2)^2 = 4π square feet.
The curved surface of the cylinder can be thought of as a rectangle that wraps around the circumference of the circle. The length of the rectangle is the circumference of the circle, and the width is the height of the cylinder (8 feet).
The circumference of a circle is found using the formula C = 2πr.
Given that the radius of the tank is 2 feet:
C_circle = 2π(2) = 4π feet.
The area of the curved surface is:
A_curved surface = C_circle * height = 4π * 8 = 32π square feet.
The total surface area of the tank is the sum of the areas of the top and bottom circles and the curved surface:
Total surface area = 2(A_circle) + A_curved surface
= 2(4π) + 32π
= 8π + 32π
= 40π square feet.
Since one gallon of paint covers 350 square feet, we can divide the total surface area of the tank by 350 to find the number of gallons needed. Then we can convert gallons to cans (assuming one gallon equals one can).
Number of cans = (Total surface area / 350) gallons
= (40π / 350) gallons
≈ 0.1143π gallons.
Given that π ≈ 3.14, the number of cans needed is:
≈ 0.1143 * 3.14
≈ 0.359202 cans.
Rounding up to the nearest whole can, Mr. Edwards will need approximately 1 can of paint.