Find the surface area of the tank?

Question

Consider a cylindrical tank with a diameter of 10 meters and a height of 15 meters. Calculate the following:

1. The total surface area of the tank, including both the curved surface area and the area of the two circular bases.

2. The volume of liquid that the tank can hold if it is filled to a height of 12 meters.

3. If the tank is to be painted on the outside, and the cost of painting is $5 per square meter, what will be the total cost of painting the tank?

To solve these questions, utilize the formulas for the surface area and volume of a cylinder:

1. Surface area \( = 2\pi rh + 2\pi r^2 \)

2. Volume \( = \pi r^2 h \)

Substitute the given values to find the required answers. Ensure to calculate each part accurately and provide the final answers with appropriate units and rounding as necessary.

Answer 1

1. To find the total surface area of the tank, including both the curved surface area and the area of the two circular bases, we use the formula: Surface area = 2πrh + 2πr^2

   
   

   Given: Diameter (d) = 10 meters (So, radius, r = d/2 = 10/2 = 5 meters) Height (h) = 15 meters

   
   

   Substituting the values: Surface area = 2π * 5 * 15 + 2π * 5^2 = 150π + 50π = 200π

   
   

   Therefore, the total surface area of the tank is 200π square meters.

2. To find the volume of liquid that the tank can hold if it is filled to a height of 12 meters, we use the formula: Volume = πr^2h

   
   

   Given: Height (h) = 12 meters

   
   

   Substituting the values: Volume = π * 5^2 * 12 = 300π

   
   

   Therefore, the tank can hold 300π cubic meters of liquid.

3. If the tank is to be painted on the outside, and the cost of painting is $5 per square meter, the total cost of painting the tank can be calculated by multiplying the surface area by the cost per square meter.

   
   

   Total cost = Surface area * Cost per square meter = 200π * $5 = 1000π dollars

   
   

   Therefore, the total cost of painting the tank will be 1000π dollars.