A water tank is in the shape of a right circular cylinder. The diameter is 8 feet, and the height is 21.5 feet. Find the surface area of the water tank. Use 3.14 for π.(1 point)
feet2
To find the surface area of the water tank, we need to find the lateral surface area (the curved surface) and the area of the top and bottom circles.
1. Lateral surface area:
The lateral surface area of a cylinder is given by the formula:
Lateral Surface Area = 2πrh
where r is the radius of the cylinder and h is the height.
Given that the diameter is 8 feet, the radius (r) is half of the diameter, so r = 8/2 = 4 feet. The height (h) is 21.5 feet.
Plugging in the values:
Lateral Surface Area = 2 * 3.14 * 4 * 21.5
Lateral Surface Area = 538.68 feet²
2. Top and Bottom circles:
The area of a circle is given by the formula:
Area = πr^2
For one circle (top or bottom), the radius is 4 feet.
Plugging in the values:
Area of one circle = 3.14 * 4^2
Area of one circle = 3.14 * 16
Area of one circle = 50.24 feet²
Since there are two circles (top and bottom), the total area for both circles is:
Total area of both circles = 2 * 50.24
Total area of both circles = 100.48 feet²
Adding the lateral surface area and the area of both circles:
Surface Area = 538.68 + 100.48
Surface Area = 639.16 feet²
Therefore, the surface area of the water tank is 639.16 square feet.