Home › Kerala SSLC (Class 10) › mathematics › Cones › The central angle of the sector required to make…
The central angle of the sector required to make a cone with base radius r and slant height l equals:
Answer & Solution
Correct answer: A.
1. The sector's arc length equals the base circumference of the cone, 2πr.
2. The full circle from which the sector is cut has radius l and circumference 2πl.
3. The arc-to-full ratio is r/l, so the central angle is r/l of the full 360°.
4. Hence central angle = 360 × r/l degrees.
5. Equivalently, the cone makes a sector that is the fraction r/l of the disc.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7-8 (pp 180-199, 2019 ed.)._
Related questions
Two cones have equal volumes. Their base radii are in the ratio 4 : 5. The ratio of their A cylindrical block of wood has base radius 15 cm and height 40 cm. The volume of the largThe volume of a cone with base radius 4 cm and height 6 cm equals:The volume of a cone with base radius r and vertical height h equals:A conical hat is to have base radius 8 cm and slant height 30 cm. Paper area required is aThe curved (lateral) surface area of a cone with base radius r and slant height l is:For a cone of base radius 5 cm and vertical height 10 cm, the slant height is:When a sector of central angle 45° is cut from a circle of radius 12 cm and rolled into a