Question

A road pylon approximates a right cone with perpendicular height 53 cm and base diameter 18 cm. The lateral surface of the pylon is to be painted with reflective paint. What is the area that will be painted?

Answer 1

The lateral surface area of the road pylon to be painted with reflective paint is approximately 1528.86 cm², which is calculated using the formula for the lateral surface area of a cone with the given dimensions.

Step-by-step explanation:

To calculate the area that needs to be painted, we must find the lateral surface area of the cone. This is given by the formula A = πrl, where r is the radius of the base of the cone and l is the slant height of the cone. First, we need to find the slant height using the Pythagorean theorem.

Given the perpendicular height (h) is 53 cm and the radius (r), which is half of the base diameter, is 9 cm, we can find the slant height (l) by calculating l = √(r² + h²).

Thus, l = √(9² + 53²) = √(81 + 2809) = √(2890) ≈ 53.76 cm.

Now we can find the lateral surface area A, A = π * 9 cm * 53.76 cm ≈ 1528.86 cm².

Therefore, the area that will be painted with reflective paint is approximately 1528.86 cm².