Find the lateral surface area and surface area of a cone with a slant height of 12in and a base radius of 4in.Use the value 3.14 for π, and do not do any rounding.Be sure to include the correct unit in your answers.

To find the lateral surface area and the total surface area of a cone, we use the following formulas:

1. Lateral Surface Area (LSA) = π * r * l, where r is the radius and l is the slant height.
2. Total Surface Area (TSA) = LSA + Base Area, where the base area of a cone is π * r^2.

Given: r = 4 in l = 12 in π = 3.14

Step 1: Calculate the Lateral Surface Area (LSA) LSA = π * r * l LSA = 3.14 * 4 in * 12 in LSA = 150.72 square inches

Step 2: Calculate the Base Area Base Area = π * r^2 Base Area = 3.14 * (4 in)^2 Base Area = 3.14 * 16 square inches Base Area = 50.24 square inches

Step 3: Calculate the Total Surface Area (TSA) TSA = LSA + Base Area TSA = 150.72 square inches + 50.24 square inches TSA = 200.96 square inches

So, the lateral surface area of the cone is 150.72 square inches and the total surface area is 200.96 square inches.