Multiple choice

For finding total surface area of cone? Which of the given expressions are required? (I) The area of the base of the cone is $1386\ cm^{2}$. (II) The curved surface area of the cone is $2310\ cm^{2}$. (III) The volume of the cone is $3696\ cm^{3}$.

  1. I and either II or III

  2. II and either I or III

  3. III and either or I or II

  4. Any two of the three
Reveal answer Fill a bubble to check yourself
D Correct answer
AI explanation

The total surface area of a cone is the sum of its base area and its curved surface area, so knowing statements I and II directly provides the answer by addition. If you know the base area (I), you can find the base radius, and combining this with the volume (III) allows you to calculate the height using the volume formula, which subsequently lets you find the slant height and the curved surface area. Similarly, knowing the curved surface area (II) and volume (III) allows you to solve a system of equations to find the radius and slant height, which then gives you the base area; therefore, any two of the three given statements are sufficient.

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