Multiple choice

A cone of height $8m$ has a curved surface area $188.4{m}^{2}$. The radius of the base is: (Take $\pi=3.14$):

  1. $4m$
  2. $4.5m$
  3. $5m$
  4. $6m$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Curved surface area of a cone = pi * r * l = 188.4. l = sqrt(r^2 + h^2). 3.14 * r * sqrt(r^2 + 8^2) = 188.4. r * sqrt(r^2 + 64) = 60. Square both sides: r^2(r^2 + 64) = 3600. Let u = r^2: u^2 + 64u - 3600 = 0. (u + 100)(u - 36) = 0. u = 36, so r = 6.

AI explanation

The formula for the curved surface area of a cone is pi * r * l, where l is the slant height, so setting this equal to 188.4 gives 3.14 * r * l = 188.4. Dividing 188.4 by 3.14 shows that r * l equals 60. Using the Pythagorean theorem for the cone's dimensions, l = sqrt(r^2 + h^2) = sqrt(r^2 + 64), and substituting this into the equation gives r * sqrt(r^2 + 64) = 60. Testing the given values, if r = 6, then l = 10, which perfectly satisfies r * l = 60, so the radius is 6 m.

Keep practicing — related questions