how to find the surface area of a cone with a diameter of 8 and a slant height of 7?
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USING DIAMETER NOT RADIOS
To find the surface area of a cone, you need to know the diameter and slant height. Here's the step-by-step explanation to help you find the surface area of a cone with a diameter of 8 and a slant height of 7:
Step 1: Find the radius:
The diameter is given as 8, so to find the radius, divide the diameter by 2:
Radius = Diameter / 2 = 8 / 2 = 4
Step 2: Find the lateral surface area of the cone:
The lateral surface area (LSA) comprises the curved surface of the cone, excluding the base. The formula for the LSA of a cone is LSA = π * radius * slant height.
LSA = π * 4 * 7 = 28π square units
Step 3: Find the base area of the cone:
The base of the cone is a circle, and the formula for the area of a circle is A = π * radius^2.
Therefore, the base area is A = π * 4^2 = 16π square units.
Step 4: Find the total surface area of the cone:
The total surface area (TSA) of the cone is the sum of the lateral surface area and the base area:
TSA = LSA + base area = 28π + 16π = 44π square units.
So, the surface area of the given cone is 44π square units.