An open cylindrical tank has an internal diameter of 5.6 cm and an internal height of 4 cm. The inside of the tank was painted. What area of the tank, in square centimeters
the surface is a circle plus the lateral area
pi*2.8^2 + pi*5.6*4
55.04
To find the area of the inside of the tank, we need to calculate the surface area of the cylinder, which consists of the lateral surface area and the two circular base areas.
The lateral surface area (A_lateral) of a cylinder can be calculated using the formula:
A_lateral = 2 * π * r * h,
where r is the radius of the cylinder and h is the height.
First, we need to find the radius (r) of the cylinder. The diameter (d) is given as 5.6 cm, so we can divide it by 2 to get the radius:
r = d/2 = 5.6 cm / 2 = 2.8 cm.
Next, we can substitute the values of the radius and height into the formula:
A_lateral = 2 * π * 2.8 cm * 4 cm.
The circular base areas can be calculated using the formula:
A_base = π * r^2.
We have the radius as 2.8 cm, so we can calculate:
A_base = π * (2.8 cm)^2.
Finally, we can sum up the lateral surface area and the two base areas to obtain the total surface area (A_total) of the inside of the tank:
A_total = A_lateral + 2 * A_base.
By substituting the values, we can calculate the area of the inside of the tank in square centimeters.