By Carla Kirkland, Chan Cleveland

The best cones are those filled with chocolate ice cream. The second-best—well, a distant second—are the ones you’ll find on the Praxis Core exam.

As you’ll see in the following practice questions, you may be asked to calculate a cone’s surface area (in this case, based on its lateral area and base area) or its volume (in this case, given its radius and slant height).

Practice questions

  1. A cone has a lateral area of PRAXIS_3401 and a base area of PRAXIS_3402.

    How many square centimeters is the surface area of the cone?


    Refer to the following figure for the next question.


  2. What is the volume of the cone?


Answers and explanations

  1. The correct answer is Choice (E).

    The surface area of a cone is the sum of its lateral area (L) and base area. A cone has only one base, so you add B to the lateral area instead of 2B.


    The surface area of the cone is


  2. The correct answer is Choice (B).

    The volume of a cone is a third of the product of its base and its height. The height of this cone isn’t given, but you can use the Pythagorean theorem to find it. The height, a radius, and the slant height form a right triangle in which the height and the radius are perpendicular and the slant height is the hypotenuse.


    The height of the cone is 24 m. That times a third of the base area is the volume of the cone:


    The volume of the cone is