Find the surface area of a cylinder with a height of 12 m and a demeanor of 15 m is 3.14 for pi and around to the nearest tenth
To find the surface area of a cylinder, we need to calculate the areas of its two circular bases and its curved surface.
First, let's calculate the area of the circular base. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. In this case, the diameter is given, which is 15 m. The radius is half of the diameter, so the radius (r) would be 15 m / 2 = 7.5 m.
Therefore, the area of one circular base is:
A_base = π(7.5 m)^2
Next, let's calculate the area of the curved surface. The formula for the lateral surface area of a cylinder is A_lateral = 2πrh, where r is the radius and h is the height.
Therefore, the area of the curved surface is:
A_curved_surface = 2π(7.5 m)(12 m)
Now, let's calculate the surface area by summing the areas of the two circular bases and the curved surface:
Surface area = 2(A_base) + A_curved_surface
Plugging in the values we calculated:
Surface area = 2(π(7.5 m)^2) + 2π(7.5 m)(12 m)
Calculating this expression, we get:
Surface area ≈ 2(3.14)(7.5 m)^2 + 2(3.14)(7.5 m)(12 m)
Surface area ≈ 2(3.14)(56.25 m^2) + 2(3.14)(90 m^2)
Surface area ≈ 2(176.625 m^2) + 2(283.2 m^2)
Surface area ≈ 353.25 m^2 + 566.4 m^2
Surface area ≈ 919.65 m^2
Rounding this to the nearest tenth, the surface area of the cylinder is approximately 919.7 m^2.