FTCE General Knowledge Math Practice Test

Which formula would be used to find the lateral area of a cone or pyramid?

1. 1/2PI

2. (3.14)r^2

3. Sum of lengths of sides

4. 1/2PI + B

The correct answer is: 1/2PI

The formula for finding the lateral area of a cone or a pyramid is not represented correctly in the selected answer. To clarify, the lateral area specifically relates to the areas of the sides of these shapes, excluding any bases. For a cone, the lateral area can be calculated using the formula \( \pi r l \), where \( r \) is the radius of the base and \( l \) is the slant height. This formula accounts for the curved surface of the cone. In the case of a pyramid, the lateral area can be computed by summing the areas of the triangular faces. The formula for this is generally \( \frac{1}{2} \times \text{perimeter of the base} \times \text{slant height} \). Looking at the provided choices, while none accurately reflect the required formulas for the lateral area of a cone or pyramid, understanding that the lateral area pertains to the surface area excluding the base is crucial. The correct approach would involve identifying either the specific lateral area formula for a cone or the appropriate calculation method for a pyramid's lateral area. To improve understanding, it’s beneficial to remember that while lateral area considers only the sides, surface area includes both bases and lateral surfaces.