Each edge of an equilateral triangle is 'a' cm A cone is formed by joining any two sides of - Maths - Heron\s Formula

Question

Each edge of an equilateral triangle is 'a' cm A cone is formed by
joining any two sides of the triangle What is the volume (in
cm3) of the cone?
(A) a 2 24 π 3 4 - π 2 (B) a 3 24 π 2 4 π 2 - 1
(C) a 3 8 π 2 1 - 4 π 2 (D) a 3 3 π 2 1 - 2 π

Amrit Lal · Answer

Base C of Cone = a cm, Slant Height = a cm
Thus 2Pie R = a or R = a/2Pie cm
Slant Height2 - (R)2 = Height2
Thus H = Root(a2 -R/22 ) = Root(a2 -
a2/(4PIE2)
Volume = 1/3PIE R2H
=1/3 PIE(a/2PIE)2 * Root [a2
-a2/(4PIE2]
=1/3 PIE*a2/4PIE2 * Root
[(4PIE2a2 -
a2)/4PIE2]
= 1/3(a2/4PIE) * a/2PIE * Root(4PIE2 - 1)
=
1/24(a2/PIE2)Root(4PIE2 - 1)
ANSWER B

Each edge of an equilateral triangle is 'a' cm. A cone is formed by joining any two sides of the triangle. What is the volume (in cm3) of the cone? (A) a 2 24 π 3 4 - π 2 (B) a 3 24 π 2 4 π 2 - 1 (C) a 3 8 π 2 1 - 4 π 2 (D) a 3 3 π 2 1 - 2 π