Question

A cylinder has a diameter of 4 m and a height of 2 m. What is the surface area of the cylinder?

16π m³
8π, m³
12π, m³
128π, m³

Answer 1

Answer:
`16\pi`

Explanation:

The equation for the surface area of a cylinder is
`2\pi r^2 + 2\pi rh`

and the equation to find the radius (r) is diameter divided by 2 so
`(d)/(2)`.

We know that...

• r =
  `(4)/(2)` = 2m

• h = 2m

so the full equation would be
`2\pi (2)^2 + 2\pi (2) (2) = 16\pi`

Answer 2

The surface area of a cylinder can be calculated by adding the area of the top and bottom circles to the area of the curved surface. The diameter of the cylinder is 4 meters, which means the radius is 2 meters. The area of a circle can be calculated using the formula A = πr².

The area of each circle is:

A = πr² = π(2m)² = 4π m²

The area of the curved surface is the circumference of the circle (2πr) multiplied by the height (2m):

A = 2πrh = 2π(2m)(2m) = 8π m²

Therefore, the total surface area of the cylinder is:

A = 2A_circle + A_curved surface
A = 2(4π m²) + 8π m²
A = 8π m² + 8π m²
A = 16π m²

So the surface area of the cylinder is 16π square meters. Therefore, the answer is a. 16π m².