2023 · Q52
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?
Elementary MathematicsMensuration
- A20 cm
- B18 cm
- C12 cm
- D9 cm
Explanation
The circumferences give top radius r = 30/(2π) and bottom radius R = 40/(2π), so r/R = 3/4. If the completed cone's vertex is v cm above the top end, similar triangles give r/R = v/(v + 6), i.e. 3/4 = v/(v+6). Solving: 3v + 18 = 4v, so v = 18 cm. The answer is (B).