HardMathematicsHigh School (9–10)Mensuration › Surface Areas and VolumesNumericalConceptualBoard Exam SAT

The frame of a lampshade is a frustum with bottom radius 20 cm, top radius 8 cm and height 9 cm…

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The frame of a lampshade is a frustum with bottom radius $20\ \text{cm}$ , top radius $8\ \text{cm}$ and height $9\ \text{cm}$ . A designer cuts the cloth as a ring-shaped piece of a circle. Find the inner and outer radii of the ring, and the angle at its centre.

Need a reminder? The key ideaShow

A frustum has bottom radius $R$ , top radius $r$ and height $h$ . Its slant height is $l = \sqrt{h^2 + (R - r)^2}$ . The complete cone has height $H = \dfrac{hR}{R - r}$ and slant height $L = \dfrac{lR}{R - r}$ . The small cone cut off is similar to the complete cone, so $\dfrac{r}{R} = \dfrac{H - h}{H}$ .

The worked solution

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