What is the surface area of a conical grain storage tank that has a height of 32 meters and a diameter of 12 meters? Round to the nearest square meter.

Answer 1

The formula for the surface area of a cone is:

A = πr^2 + πr√(r^2 + h^2)

Where r is the radius of the base of the cone and h is the height of the cone.

Given that the diameter of the cone is 12 meters, the radius (r) is half of the diameter, so r = 12/2 = 6 meters.

Plugging in the values of r = 6 meters and h = 32 meters into the formula, we get:

A = π(6)^2 + π(6)√(6^2 + 32^2)
A = π(36) + π(6)√(36 + 1024)
A = 36π + 6π√1060
A ≈ 36π + 6π(32.57)
A ≈ 36π + 197.2π
A ≈ 233.2π

To get the surface area to the nearest square meter, we need to calculate the value of π:

π ≈ 3.14159

Therefore, the surface area of the conical grain storage tank is approximately:

A ≈ 233.2 * 3.14159
A ≈ 733.31 square meters

Rounded to the nearest square meter, the surface area of the conical grain storage tank is 733 square meters.