Answer to Question #149994 in Trigonometry for yui

Question

PROBLEM 4. In a frustum of right circular cone the altitude is 3 cm and the radii of the bases are 2 cm and 6 cm. Find the lengths of the slant height and altitude of the entire cone of which this frustum is a part.
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Answer 1

Solution:

$from\, similar\, triangles, \\ \frac{x}{x+3} = \frac{2}{6} \\ 6x = 2x + 6 \\ x = \frac{6}{4} \Rightarrow \frac{3}{2}cm \\ h = \frac{3}{2} + 3 \Rightarrow\frac{9}{2}cm \\ by\, pythagoras\, theorem, \\ l^2 = h^2 + 6^2 \\ l^2 = (\frac{9}{2})^2 + 6^2\\ l^2 = \frac{81}{4} + 36 =\frac{225}{4}\\ \therefore l = \sqrt{\frac{225}{4}} = \frac{15}{2}cm$