Multiple choice

The ratio of the ratii of two circular cones of hte same height is 1 : 2 and height of each come is $\displaystyle \sqrt{3}$ times the smaller radius then curved surface areas of two cones will be the ratio of

  1. 2 : 5
  2. $\displaystyle 10:2\sqrt{3}$
  3. $\displaystyle 1:\sqrt{7}$

  4. 3 : 2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Interpret the garbled wording as the cones having radii in the ratio 1:2 and equal height h = sqrt(3)r, where r is the smaller radius. Their slant heights are 2r and sqrt(7)r. Since curved surface area is proportional to radius x slant height, the ratio is 1:sqrt(7).

AI explanation

Let the radii of the two cones be 1 and 2, so their heights are both root 3. The slant heights are calculated using the Pythagorean theorem as root of 1 squared plus root 3 squared, which is 2 for the first cone, and root of 2 squared plus root 3 squared, which is root 7 for the second. The curved surface area formula is pi times radius times slant height, making the ratio of their curved surface areas (1 times 2) : (2 times root 7), which simplifies to 1 : root 7.

Keep practicing — related questions