Multiple choice

What is the volume of a cone, if its radius is 9 cm and its curved surface area is 423.9 cm2? (Use pi = 3.14)

  1. 1014.24 cm3

  2. 1017.36 cm3

  3. 1022.15 cm3

  4. 1025.67 cm3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Curved surface area = pi * r * l = 423.9. 3.14 * 9 * l = 423.9, so l = 423.9 / 28.26 = 15. Height h = sqrt(l^2 - r^2) = sqrt(225 - 81) = sqrt(144) = 12. Volume = (1/3) * pi * r^2 * h = (1/3) * 3.14 * 81 * 12 = 3.14 * 81 * 4 = 1017.36.

AI explanation

Using the curved surface area formula for a cone, the area equals pi times r times l, where r is the radius and l is the slant height. Substituting the given values, we get 423.9 = 3.14 times 9 times l, which makes l = 15 cm. Applying the volume formula, the volume is one third times pi times r squared times height, so we find the height h using l squared = r squared + h squared, yielding h = sqrt(225 minus 81) = 12 cm. Therefore, the volume is 1/3 times 3.14 times 81 times 12, which equals 1017.36 cm3.

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