A cone has a base radius of 3 m and a height of 4 m. What is the surface area of the cone?

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Questions & Step-by-step Solutions

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Q: A cone has a base radius of 3 m and a height of 4 m. What is the surface area of the cone?

Solution: The surface area of a cone is given by SA = πr(r + l), where l is the slant height. Here, l = √(3² + 4²) = 5, so SA = π(3)(3 + 5) = 24π.

Steps: 8

Step 1: Identify the formula for the surface area of a cone, which is SA = πr(r + l).
Step 2: Find the radius (r) of the cone, which is given as 3 m.
Step 3: Find the height (h) of the cone, which is given as 4 m.
Step 4: Calculate the slant height (l) using the formula l = √(r² + h²).
Step 5: Substitute the values into the formula for slant height: l = √(3² + 4²) = √(9 + 16) = √25 = 5 m.
Step 6: Substitute the values of r and l into the surface area formula: SA = π(3)(3 + 5).
Step 7: Simplify the expression: SA = π(3)(8) = 24π.
Step 8: The surface area of the cone is 24π square meters.

A cone has a base radius of 3 m and a height of 4 m. What is the surface area of the cone?

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