A cone has a base radius of 4 cm and a height of 9 cm. What is the total surface

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Question: A cone has a base radius of 4 cm and a height of 9 cm. What is the total surface area of the cone?

Options:

Correct Answer: 75.36 cm²

Solution:

Total Surface Area = πr(r + l), where l = √(r² + h²) = √(4² + 9²) = √(16 + 81) = √97. Total Surface Area = π * 4 * (4 + √97).

A cone has a base radius of 4 cm and a height of 9 cm. What is the total surface area of the cone?

A cone has a base radius of 4 cm and a height of 9 cm. What is the total surface area of the cone?

Step 1: Identify the given values. The base radius (r) is 4 cm and the height (h) is 9 cm.
Step 2: Use the formula for the slant height (l) of the cone, which is l = √(r² + h²).
Step 3: Calculate r², which is 4² = 16.
Step 4: Calculate h², which is 9² = 81.
Step 5: Add r² and h² together: 16 + 81 = 97.
Step 6: Find the square root of 97 to get l: l = √97.
Step 7: Now, use the formula for the total surface area of the cone: Total Surface Area = πr(r + l).
Step 8: Substitute the values into the formula: Total Surface Area = π * 4 * (4 + √97).
Step 9: This is the final expression for the total surface area of the cone.

Surface Area of a Cone – The total surface area of a cone is calculated using the formula πr(r + l), where r is the radius and l is the slant height.
Slant Height Calculation – The slant height (l) is determined using the Pythagorean theorem, l = √(r² + h²), where h is the height of the cone.