A cone has a base radius of 5 cm and a height of 12 cm. What is its surface area

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Question: A cone has a base radius of 5 cm and a height of 12 cm. What is its surface area?

Options:

Correct Answer: 65π cm²

Solution:

The surface area of a cone is given by SA = πr(r + l), where l is the slant height. Here, l = √(5² + 12²) = 13, so SA = π(5)(5 + 13) = 90π cm².

A cone has a base radius of 5 cm and a height of 12 cm. What is its surface area?

A cone has a base radius of 5 cm and a height of 12 cm. What is its surface area?

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 5 cm.
Step 3: Find the height (h) of the cone, which is given as 12 cm.
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 = √(5² + 12²) = √(25 + 144) = √169 = 13 cm.
Step 6: Substitute r and l into the surface area formula: SA = π(5)(5 + 13).
Step 7: Calculate the expression inside the parentheses: 5 + 13 = 18.
Step 8: Multiply: SA = π(5)(18) = 90π cm².

Surface Area of a Cone – The formula for the surface area of a cone involves the base radius and the slant height, which is derived from the Pythagorean theorem.
Slant Height Calculation – Understanding how to calculate the slant height using the radius and height of the cone.