Answer :
The area of the base of the cylindrical metal tank is calculated using the volume and height given. By converting liters to cubic meters and using the formula for the volume of a cylinder, the radius is found, which is then used to calculate the base area. You would need 1.5 square meters of metal sheet for the base.
To find out how many square meters of metal sheet would be needed to make the base of the cylindrical metal tank, we need to calculate the area of the base of the cylinder.
Since we are given the capacity of the cylinder in liters and the height in meters, we first convert the capacity into cubic meters because 1 liter equals 0.001 cubic meters. Therefore, 1500 liters are equivalent to 1.5 cubic meters.
The formula for the volume of a cylinder is V = (πR²h), where V is the volume, R is the radius, h is the height, and π (pi) is approximately 3.141592653589793. We have V as 1.5 cubic meters and the height h as 1 meter.
We can solve for R² and then find R, which will then allow us to calculate the area of the base using the formula A = πR².
Let's solve for the radius step-by-step:
- Volume formula: V = πR²h
- Substitute V with 1.5 m³ and h with 1 m: 1.5 = πR²(1)
- R² = 1.5 / π
- Find R: R = sqrt(1.5 / π)
- Calculate the area of the base: A = πR² = π(sqrt(1.5 / π))²
- Simplify: A = 1.5 square meters
Therefore, you would need 1.5 square meters of metal sheet to make the base of the tank.
