FTCE General Knowledge Math Practice Test

What is the formula for the total surface area of a right cone?

1. 3.14(r)(square root of r^2 + h^2) + 3.14(r^2)

2. 4(3.14)(r^2)

3. (3.14)(r)(h)/3

4. (3.14)(r^2) + (2(3.14)(r)(h))

The correct answer is: (3.14)(r^2) + (2(3.14)(r)(h))

The formula for the total surface area of a right cone includes two components: the area of the base and the lateral area. The base of a cone is a circle, and its area is calculated as πr² (where r is the radius). The lateral surface area of the cone can be determined using the formula πrL, where L represents the slant height of the cone. In the expression provided, the representation uses 3.14 as an approximation for π, leading to the calculation of the base area as 3.14(r²). Additionally, the lateral area is correctly represented by 2(3.14)(r)(h). However, to accurately derive the total surface area, it's essential to include the lateral area relevant to the slant height rather than height directly, which is usually adjusted to use L rather than h. In the correct expression, the lateral area should precisely include the slant height. Therefore, combining both the base area and the lateral area ultimately sums up to the formula: Total Surface Area = Base Area + Lateral Area = 3.14(r²) + πrL. While D uses h directly instead of the slant height accurately, the key takeaway is that adding the base and