If the development of the lateral surface of a cone is a semicircle, then : (a) the slant height of the cone < diameter of the base of the cone
Answers
The options given are:
a. The slant height of the cone < diameter of the base of the cone
b. The slant height of the cone > diameter of the base of the cone
c. The slant height of the cone = diameter of the base of the cone
d. The slant height of the cone = radius of the base of the cone
Answer is - c
The slant height of the cone = diameter of the base of the cone
q = r / l x 360 degrees
l = d = 2r
q = 180 degrees
Since the options are not given, have given the options below. The correct option is “C”.
"When the curved surface of a cone is opened and laid on a plane, it shows the shape of a sector. The included angle of the sector depends on the slant height, Rand the radius of the base of the cone, r. The radius of the sector will be equal to the slant height of the cone. The length of the arc will be equal to the circumference of the base of the cone, i.e. 2πr. If θ is the included angle (in radian) of the sector, then, R θ= 2πr."
The options given are:
a. The slant height of the cone < diameter of the base of the cone
b. The slant height of the cone > diameter of the base of the cone
c. The slant height of the cone = diameter of the base of the cone
d. The slant height of the cone = radius of the base of the cone