Final Answer:
The surface area of the cone is 469.47πm².
Step-by-step explanation:
To find the surface area of the cone, we use the formula 4πr2 + πrl, where r is the radius and l is the slant height. The given cone has a radius of 20πm and a slant height of 42πm. Thus, the surface area of the cone is 4π(20πm)2 + π(20πm)(42πm), which is equal to 469.47πm².
To find the volume of the cone, we use the formula V = 1/3 πr2h, where r is the radius and h is the height. The given cone has a radius of 20πm and a height of 36πm. Thus, the volume of the cone is 1/3 π(20πm)2(36πm), which is equal to 6144πm³.
To find the curved surface area of the cone, we use the formula A = πrl, where r is the radius and l is the slant height. The given cone has a radius of 20πm and a slant height of 42πm. Thus, the curved surface area of the cone is π(20πm)(42πm), which is equal to 840πm².
To find the base area of the cone, we use the formula A = πr2, where r is the radius. The given cone has a radius of 20πm. Thus, the base area of the cone is π(20πm)2, which is equal to 400πm².
The surface area of the cone is the sum of the curved surface area and the base area of the cone. Thus, the surface area of the cone is 469.47πm², which is equal to 840πm² + 400πm².