Multiple choice

Find the slant height of a cone whose, Base radius $=14\;cm$, height $0.48\;m$ Base diameter $=70\;cm$, curved surface area $=4070\;cm^2$

  1. $52\;cm\;;\;37\;cm$
  2. $50\;cm\;;\;37\;cm$
  3. $51\;cm\;;\;37\;cm$
  4. $50\;cm\;;\;36\;cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The prompt combines two cone datasets. For radius 14 cm and height 48 cm, the slant height is sqrt(14^2 + 48^2) = 50 cm. For diameter 70 cm and curved surface area 4070 cm^2, the slant height is 37 cm, so the paired answer is B.

AI explanation

For the first cone, we convert the height 0.48 m to 48 cm and apply the Pythagorean theorem for slant height, l = sqrt(r^2 + h^2). Substituting the values gives sqrt(14^2 + 48^2) = sqrt(196 + 2304) = sqrt(2500), which equals 50 cm. For the second cone, the curved surface area formula is pi * r * l = 4070. Using the radius from the base diameter (70/2 = 35 cm), we solve (22/7) * 35 * l = 4070 to get 110 * l = 4070, which results in a slant height of 37 cm.

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