The height of a cone is 7 inches, and the radius is 4...

The height of a cone is 7 inches, and the radius is 4 inches. Round final answers to the nearest ten-thousandth.
Round the slant height to the nearest hundredth and then calculate the lateral area of the cone.

Key Concepts

Lateral Surface Area

The lateral surface area of a cone refers to the area of the curved surface that connects the base to the vertex. It is calculated by multiplying the base's circumference by the slant height and then halving the result, which involves both geometric and algebraic manipulation.

Slant Height

The slant height of a cone is the distance measured along the lateral side from the top (vertex) to the edge of the base. It is calculated using the Pythagorean theorem and is a critical component in determining the lateral surface area of the cone.

Rounding

Rounding is a numerical process used to simplify a number to a specific degree of precision. This concept is crucial when final answers require standardization of significant figures, such as rounding the slant height to the nearest hundredth or final results to the nearest ten-thousandth.

Cone

A cone is a three-dimensional geometric shape characterized by a circular base and a vertex that is not in the plane of the base. It features a curved surface that tapers smoothly from the base to the vertex, which is essential in problems dealing with volume and surface area calculations.

Pythagorean Theorem

The Pythagorean theorem is a fundamental principle in geometry used to calculate the relationship between the sides of a right triangle. In the context of cones, it is used to determine the slant height by relating the height and the radius of the cone.

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