A wooden toy is shaped like a rocket with a cone mounted on a cylinder. The total height of the rocket is 26 cm, while the height of the conical part is 8 cm. The base of the conical portion has a diameter of 12 cm, while the base diameter of the cylindrical portion is 6 cm. The conical portion is to be painted orange and the cylindrical portion yellow. Which of the following statements is correct regarding the orange-painted area?

Question

Quintessence Classes · Accepted Answer

The correct answer is The orange area is calculated as (CSA of cone) + (Base area of cone - Base area of cylinder). The correct statement is C) The orange area is calculated as (CSA of cone) + (Base area of cone - Base area of cylinder).ExplanationTo understand why option C is correct, consider which parts of the conical top are exposed to be painted orange:Curved Surface Area (CSA) of the Cone: The entire slanted outer surface of the cone is exposed and must be painted orange.Base of the Cone: Since the base of the cone (12 cm diameter) is wider than the top of the cylinder (6 cm diameter), the cylinder does not cover the entire bottom of the cone.Overlapping Base Region: The base of the cylinder attaches to the center of the cone's base. The region where they overlap is hidden and attached to the cylinder, leaving a ring-shaped surface around the cylinder that is exposed on the underside of the cone.Therefore, the total area to be painted orange equals the curved surface area of the cone plus the exposed ring at the bottom, which is calculated by subtracting the base area of the cylinder from the base area of the cone.

Answer

The orange area is simply the Curved Surface Area (CSA) of the cone

Answer

The orange area is the sum of the CSA of the cone and the area of the base of the cone

Answer

The orange area is calculated as (CSA of cone) + (CSA of cylinder)

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