A cylinder is 12cm tall and has a diameter of 3 cm. What is the surface area?
A=2πrh+2πr2
A = (2 * 3.14 * 1.5 * 12) + (2 * 3.14 * 1.5 * 1.5)
To find the surface area of a cylinder, we need to calculate the areas of the two circular bases and the lateral surface area.
First, let's start by finding the area of one of the circular bases. The formula for the area, A, of a circle is given by A = πr², where r is the radius.
Given that the diameter of the cylinder is 3 cm, we can find the radius by dividing the diameter by 2. So the radius, r, is 3 cm / 2 = 1.5 cm.
Now, we can calculate the area of one circular base using the formula:
A_base = πr² = π(1.5 cm)²
Next, let's calculate the lateral surface area of the cylinder. The formula for the lateral surface area, S, of a cylinder is given by S = 2πrh, where r is the radius and h is the height.
In this case, the height of the cylinder is given as 12 cm, and we already found the radius (1.5 cm). So, we can calculate the lateral surface area using the formula:
S_lateral = 2πrh = 2π(1.5 cm)(12 cm)
Finally, to find the total surface area, we add the areas of the two circular bases and the lateral surface area:
Total Surface Area = 2A_base + S_lateral = 2(πr²) + 2πrh
Now, we can substitute the values we calculated to find the solution:
Total Surface Area = 2(π(1.5 cm)²) + 2π(1.5 cm)(12 cm)
Calculating this expression will give us the surface area of the cylinder.