What is the total surface area in square cm of a closed cylinder that is 12 cm high and 3 cm in diameter?

To determine the total surface area of a closed cylinder, you need to consider both the lateral surface area and the areas of the top and bottom circular bases.

The formula for the total surface area (A) of a closed cylinder is given by:

[

A = 2\pi r h + 2\pi r^2

]

where (r) is the radius of the base, and (h) is the height of the cylinder.

In this case, the diameter of the cylinder is 3 cm, which means the radius (r) is half of that, or 1.5 cm. The height (h) is given as 12 cm.

Plugging in the values:

1. Calculate the lateral surface area:

(2\pi r h = 2\pi (1.5 , \text{cm})(12 , \text{cm}) = 36\pi , \text{cm}^2).

2. Calculate the area of the top and bottom:

(2\pi r^2 = 2\pi (1.5 , \text{cm})^2 = 2\pi (2.25 \