Question

The central angle of a sector is 288° If this sector is rolled up to make a cone, find the ratio between the radius and slant height of the cone.

Answer 1

360 x \(\frac{4}{5}\) = 288

∴ Radius of the cone 4 = \(\frac{4}{5}\) x radius of the big circle

∴ If r is the radius of the circle Radius of the Radius of the cone = \(\frac{4}{5}\) r

But radius of the circle = slant height of cone

i.e., 1 = r

∴ Ratio between the radius of the cone and slant height

\(=\frac{4}{5}r:r=\frac{4}{5}:1=4:5\)