Multiple choice

The curved surface area of a right circular cone of radius 28cm is 4664 cm$^2$. What is the ratio of the volume of the cone to the total surface area of the cone ?(Use $\pi=\frac{22}{7}$)

  1. $120:37$
  2. $23:27$
  3. $100:53$
  4. $140:27$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

CSA of cone = πrl = 4664. Given r = 28, π = 22/7, so l = 4664 × 7/(22 × 28) = 53 cm. Height h = √(l² - r²) = √(2809 - 784) = √2025 = 45 cm. Volume = (1/3)πr²h = (1/3)(22/7)(784)(45) = 116160 cm³. Total surface area = πr(l + r) = (22/7)(28)(81) = 7128 cm². Ratio = 116160 : 7128 = 140 : 27 after simplification.