Answer to Question #149994 in Trigonometry for yui

Question #149994
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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Expert's answer
2020-12-17T19:01:40-0500

Solution:

"from\\, similar\\, triangles, \\\\\n\\frac{x}{x+3} = \\frac{2}{6} \\\\\n6x = 2x + 6 \\\\\nx = \\frac{6}{4} \\Rightarrow \\frac{3}{2}cm \\\\\nh = \\frac{3}{2} + 3 \\Rightarrow\\frac{9}{2}cm \\\\\nby\\, pythagoras\\, theorem, \\\\\nl^2 = h^2 + 6^2 \\\\\nl^2 = (\\frac{9}{2})^2 + 6^2\\\\\nl^2 = \\frac{81}{4} + 36 =\\frac{225}{4}\\\\\n\\therefore l = \\sqrt{\\frac{225}{4}} = \\frac{15}{2}cm"


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