Multiple choice

The cost of painting the curved surface area of a cone at $5\ ps/cm^{2}$ is $Rs 35.20$, find the volume of the cone if its slant height is $25 cm$.

  1. $1223\ cm^{3}$
  2. $1979\ cm^{3}$
  3. $1323\ cm^{3}$
  4. $1332\ cm^{3}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

At 5 paise per cm^2, a cost of Rs 35.20 corresponds to a curved surface area of 704 cm^2. Using pi r l = 704 with l = 25 cm gives r = 8.96 cm. The height is about 23.35 cm, and V = (1/3)pi r^2h is approximately 1979 cm^3.

AI explanation

Converting the cost to paise, 35.20 Rupees is 3520 paise, and dividing by the rate of 5 paise per square cm gives a curved surface area of 704 square cm. Using the formula pi r l = 704 with l = 25 gives the radius r = 704 / (22/7 times 25), which equals 8.96 cm; using the Pythagorean theorem, the height h is the square root of (25 squared - 8.96 squared), which is about 23.34 cm. Calculating the cone volume (1/3) pi r squared h results in approximately 1979 cubic cm.

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