A lamp shade is in the shape of a part of a cone and its top and bottom ends are circles whose circumferences are respectively 30 cm and 40 cm. The perpendicular distance between the ends is 6 cm. If the cone were to be completed, then how far would its vertex be from the top end?
A.20 cm
B.12 cm
C.9 cm
D.18 cm✓ Correct
Explanation
Radii r₁ = 30/(2π) and r₂ = 40/(2π). By similar triangles, h_top/(h_top+6) = r₁/r₂ = 30/40 = 3/4. 4h_top = 3h_top+18, h_top = 18 cm.
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