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?

    PRAXIS_3403

    Refer to the following figure for the next question.

    praxis-core-cone

  2. What is the volume of the cone?

    PRAXIS_3404

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.

    PRAXIS_3405

    The surface area of the cone is

    PRAXIS_3406

  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.

    PRAXIS_3407

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

    PRAXIS_3408

    The volume of the cone is

    PRAXIS_3409