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. 18 cm ✓
- C. 12 cm
- D. 9 cm
Correct Answer: B. 18 cm
Explanation
Let the distance from the vertex to the top be x. Since circumference is proportional to radius, by similar triangles we have \frac{x}{x+6} = \frac{30}{40}. Solving this gives 40x = 30x + 180 \implies 10x = 180 \implies x = 18 cm.
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