A cylinder is 12 cm tall and has a diameter of 3 cm. What is the total surface area?

Pi x radius x radius=3.14 x 1.5 x 2=9.42 cm
Pi x diameter= 3.14 x 3= 9.42cm
length x width= 9.42 x 12= 113.04cm
Total Surface Area= 9.42+9.42+113.04=131.8cmsquared.
The answer is 157cm.
I don't understand how to get the answer 157cm.

pi * 1.5 * 1.5 * 2 = 14.14

you did not square r in pi r^2

To find the total surface area of a cylinder, you need to consider two components: the lateral surface area and the base area.

1. Lateral Surface Area: The lateral surface area of a cylinder is given by the formula 2πrh, where r is the radius of the base and h is the height of the cylinder.
In this case, the radius (r) of the cylinder is half the diameter, which is 3 cm / 2 = 1.5 cm.
The height (h) of the cylinder is given as 12 cm.
Therefore, the lateral surface area = 2π(1.5 cm)(12 cm) = 36π cm^2.

2. Base Area: The base area of a cylinder is given by the formula πr^2, where r is the radius of the base.
In this case, the radius (r) of the cylinder is 1.5 cm.
Therefore, the base area = π(1.5 cm)^2 = 2.25π cm^2.

Now, to find the total surface area, you add the lateral surface area and the base areas together:
Total Surface Area = Lateral Surface Area + 2 * Base Area = 36π cm^2 + 2 * 2.25π cm^2 = 36π cm^2 + 4.5π cm^2 = 40.5π cm^2.

To find an approximate numerical value, you can use the approximation π ≈ 3.14:
Total Surface Area ≈ 40.5 * 3.14 cm^2 ≈ 127.17 cm^2.

So, the total surface area of the cylinder is approximately 127.17 cm^2, not 157 cm.

To calculate the total surface area of a cylinder, you need to find the individual areas of its curved surface and its two circular bases and then add them together.

Let's start by finding the area of the curved surface. The curved surface of a cylinder can be thought of as a rectangle that has been rolled up to form a cylinder. The height of this rectangle is the same as the height of the cylinder, which is 12 cm. The length of the rectangle is the circumference of the base, which can be found using the formula: circumference = π x diameter.

So, in this case, the circumference of the base is π x 3 cm = 9.42 cm. Therefore, the length of the rectangle is also 9.42 cm. To find the area of the curved surface, you multiply the length by the height, which gives us 9.42 cm x 12 cm = 113.04 cm².

Next, let's find the area of the two circular bases. The area of a circle is given by the formula: area = π x radius². In this case, the radius is half of the diameter, so it is 1.5 cm. Therefore, the area of one circular base is π x (1.5 cm)² = 7.065 cm². Since there are two circular bases, the total area of the bases is 2 x 7.065 cm² = 14.13 cm².

Finally, you add the area of the curved surface and the area of the bases together to get the total surface area of the cylinder: 113.04 cm² + 14.13 cm² = 127.17 cm².

Therefore, the correct answer for the total surface area of the cylinder is 127.17 cm², not 157 cm as mentioned before.