Calculating the Radius and Slant Height

Oct 13, 2025 by talynt.org 104 views

Introduction

In this article, we will explore the concept of calculating the surface area of a cone, which is a fundamental concept in mathematics. The surface area of a cone is the total area of its surface, including the base and the lateral surface. We will use the given dimensions of a cone, which is 28 inches in height and 14 inches in diameter, to calculate its surface area.

Understanding the Formula

The formula for the surface area of a cone is:

A = πr^2 + πrl

Where:

A is the surface area of the cone
π (pi) is a mathematical constant approximately equal to 3.14
r is the radius of the base of the cone
l is the slant height of the cone

Calculating the Radius and Slant Height

To calculate the surface area of the cone, we need to find the radius and slant height of the cone. The radius of the cone is half of its diameter, which is:

r = 14/2 = 7 inches

The slant height of the cone can be calculated using the Pythagorean theorem:

l = √(h^2 + r^2)

Where:

h is the height of the cone
r is the radius of the cone

Plugging in the values, we get:

l = √(28^2 + 7^2) l = √(784 + 49) l = √833 l ≈ 28.8 inches

Calculating the Surface Area

Now that we have the radius and slant height of the cone, we can calculate its surface area using the formula:

A = πr^2 + πrl

Plugging in the values, we get:

A = π(7)^2 + π(7)(28.8) A = 3.14(49) + 3.14(207.6) A = 153.86 + 650.14 A ≈ 804 in^2

Rounding to the Nearest Square Inch

The surface area of the cone is approximately 804 square inches. However, the problem asks for the answer to the nearest square inch. Rounding 804 to the nearest square inch gives us:

A ≈ 804 in^2

Conclusion

In this article, we calculated the surface area of a cone with a height of 28 inches and a diameter of 14 inches. We used the formula for the surface area of a cone and calculated the radius and slant height of the cone. We then used these values to calculate the surface area of the cone, which is approximately 804 square inches.

Discussion

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