Question : If the slant height of a cone is 29 cm and its height is 20 cm, find the ratio between the magnitudes of the total surface area and the volume.
Option 1: 5 : 14
Option 2: 7 : 15
Option 3: 3 : 7
Option 4: 3 : 14
Correct Answer: 5 : 14
Solution : Given, Slant height($l$) = 29 cm Height($h$) = 20 cm ⇒ Radius, $(r) = \sqrt{l^2-h^2}$ ⇒ $r=\sqrt{29^2-20^2}$ ⇒ $r=\sqrt{841-400}$ ⇒ $r=\sqrt{441}$ ⇒ $r=21$ cm Total surface area of cone = $ πr(r + l)$ and volume = $\frac13πr^2h$ $\therefore$ Ratio = $(r+l):(\frac13rh)=(21+29):\frac13\times21\times20=50:140=5 : 14$ Hence, the correct answer is 5 : 14.
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