a.) To find the height (h) of the cone we'll use the slant height (s) and the radius of the hemisphere (r). By Pythagorean Theorem;
s^2 = h^2 + r^2
h^2 = s^2 - r^2
h^2 = 6.1^2 - 1.1^2
h^2 = 37.21 - 1.21
h^2 = 36
h = sqrt(36)
h = 6 cm.
b.)To find the volume of crystal pendulum (V) we'll add the volume of the cone (V1) and the volume of hemisphere (V2).
V = V1 + V2
V1 = (1/3)(pi)(r^2)(h)
V1 = (1/3)(1.1^2)(6)(pi)
V1 = 2.42pi
V2 = (4/3)(pi)(r^3)(1/2) [ multiplied by 1/2 because it is a hemisphere]
V2 = (2/3)(pi)(r^3)
V2 = (2/3)(1.1^3)(pi)
V2 = 0.8873pi
V = V1 + V2
V = 2.42pi + 0.8873pi
V = 3.3073pi cm^3
V = 10.39 cm^3
