The central angle and radius of a sector of a circular disc 180° are and are 21 cm respectively. If the edges of the sector of a disc are joined together to make a hollow cone, then find the radius of the cone.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

10.5 cm

10 cm

12.5 cm

None of these

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Concept- The radius of the disc becomes the slant height of the newly created cone because the edges of the sector of a circular disc are linked together to produce the cone. The sector of the disc's surface area is equal to the cone's curved surface area.
The area of the sector of a circle with radius r and angle formed by the sector at the centre be θ is given by 360r2.
Here the angle formed by the sector of a circular disc at the centre is given to be 180∘180∘and radius of the disc is given to be 21 cm.
The area of the given sector can be calculated by substituting the value 180° for θ and 21 for r in the formula area of sector of disc = 212
The curved surface area of the cone must also be equal to the area of the sector of the circular disc.
The curved surface area of a cone is given by πRl, where R is radius of the cone and l is the slant height.
The radius of the disc becomes the slant height of the newly formed cone. Therefore, l=21
Thus the curved surface area of the cone is πR(21).
Equating the curved surface area of cone to the area of sector of circular disc,
2122=πR(21)
R=10.5
Hence, the correct option is 1) 10.5 cm

Watch 3-min video & get full concept clarity