The central angle of a circle is divided in the ratio 2 : 3 to form tw

1.	The central angle of a circle is divided in the ratio 2 : 3 to form two sectors. Two cones are made by rolling up the two Rectors. a. Find out the ratio between the base perimeters of the cones. b. What is the ratio between the curved surface areas
Answer» a. Central angles are in the ratio 2 : 3 , so, let the perimeter of the two clones which made by rolling up this two sectors be \(\frac{2}{5}\) part and \(\frac{3}{5}\) part of the perimeter of the circle That is perimeter of each sector be \(2\pi r\times\frac{2}{5}\) and \(2\pi r\times\frac{3}{5}\) Ratio between base perimeters of cone = \(2\pi r\times\frac{2}{5}\) : \(2\pi r\times\frac{3}{5}\) = 2 : 3 b. Base perimeter of the cones will be \(\frac{2}{5}\) and \(\frac{3}{5}\) parts of the circumference of the 5 circle. Ratio between the perimeters of die cones \(=\pi r^2\times\frac{2}{5}\) : \(\pi r^2\times\frac{3}{5}\) = 2; 3

The central angle of a circle is divided in the ratio 2 : 3 to form two sectors. Two cones are made by rolling up the two Rectors. a. Find out the ratio between the base perimeters of the cones. b. What is the ratio between the curved surface areas

Answer»

a. Central angles are in the ratio 2 : 3 , so, let the perimeter of the two clones which made by rolling up this two sectors be \(\frac{2}{5}\) part and \(\frac{3}{5}\) part of the perimeter of the circle

That is perimeter of each sector be \(2\pi r\times\frac{2}{5}\) and \(2\pi r\times\frac{3}{5}\)

Ratio between base perimeters of cone = \(2\pi r\times\frac{2}{5}\) : \(2\pi r\times\frac{3}{5}\) = 2 : 3

b. Base perimeter of the cones will be \(\frac{2}{5}\) and \(\frac{3}{5}\) parts of the circumference of the 5 circle.

Ratio between the perimeters of die cones \(=\pi r^2\times\frac{2}{5}\) : \(\pi r^2\times\frac{3}{5}\) = 2; 3

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