Question

Surface area of cones practice

Answer 1

To practice finding the surface area of cones, here are two sample problems with step-by-step solutions:

Problem 1: Calculate the surface area of a cone with a radius of 4 cm and a slant height of 6 cm.

Solution:
Step 1: Find the curved surface area of the cone using the formula:
Curved Surface Area = π * radius * slant height
Curved Surface Area = π * 4 cm * 6 cm = 24π cm²

Step 2: Find the base area of the cone using the formula:
Base Area = π * radius²
Base Area = π * (4 cm)² = 16π cm²

Step 3: Find the total surface area by adding the curved surface area and the base area:
Total Surface Area = Curved Surface Area + Base Area
Total Surface Area = 24π cm² + 16π cm² = 40π cm²

Therefore, the surface area of the cone is 40π cm².

Problem 2: Find the surface area of a cone with a radius of 3.5 meters and a slant height of 8 meters.

Solution:
Step 1: Calculate the curved surface area of the cone:
Curved Surface Area = π * radius * slant height
Curved Surface Area = π * 3.5 m * 8 m = 28π m²

Step 2: Determine the base area of the cone:
Base Area = π * radius²
Base Area = π * (3.5 m)² = 12.25π m²

Step 3: Add the curved surface area and the base area to find the total surface area:
Total Surface Area = Curved Surface Area + Base Area
Total Surface Area = 28π m² + 12.25π m² = 40.25π m²

Therefore, the surface area of the cone is 40.25π m².