A closed tin of milk has a diameter of 10 cm and height 16 cm , find the total surface area of the tin {take pie to be 22/7}
To find the total surface area of the tin, we need to calculate the area of each of its components and then add them up.
The total surface area of the tin can be divided into 3 parts: the top and bottom circles, and the curved surface area of the cylinder.
1. The area of each circle can be calculated using the formula for the area of a circle: A = πr^2, where A is the area and r is the radius.
The radius of the circle is half the diameter, so in this case, r = 10/2 = 5 cm.
The area of each circle is: A = (22/7) * (5)^2 = (22/7) * 25 = 78.57 cm^2.
Since there are two circles (top and bottom) in the tin, the total area of the circles is 2 * 78.57 = 157.14 cm^2.
2. The curved surface area of the cylinder can be calculated using the formula: A = 2πrh, where A is the area, r is the radius, and h is the height.
The radius of the cylinder is the same as the radius of the circles, so r = 5 cm.
The height is given as 16 cm.
The curved surface area of the cylinder is: A = 2 * (22/7) * 5 * 16 = 502.86 cm^2.
3. Finally, we add up the area of the circles and the curved surface area of the cylinder: 157.14 + 502.86 = 660 cm^2.
Therefore, the total surface area of the tin is 660 cm^2.
To find the total surface area of the closed tin of milk, we need to find the area of the top and bottom circles and the lateral surface area of the cylindrical part of the tin.
The formula for the area of a circle is given by A = πr^2, where r is the radius of the circle.
Given that the diameter of the tin is 10 cm, the radius (r) is half of the diameter, so r = 10/2 = 5 cm.
Now, let's calculate the area of the top and bottom circles:
A_top_bottom = 2πr^2
= 2 * (22/7) * 5^2
= 2 * (22/7) * 25
= (44/7) * 25
= 11 * 25
= 275 cm^2
The formula for the lateral surface area of a cylinder is given by A_lateral = 2πrh, where r is the radius and h is the height of the cylinder.
Now, let's calculate the lateral surface area of the cylindrical part of the tin:
A_lateral = 2πrh
= 2 * (22/7) * 5 * 16
= (44/7) * 5 * 16
= 11 * 5 * 16
= 880 cm^2
Finally, to find the total surface area, we need to add the area of the top and bottom circles and the lateral surface area:
Total surface area = A_top_bottom + A_lateral
= 275 + 880
= 1155 cm^2
Therefore, the total surface area of the closed tin of milk is 1155 cm^2.