Matching of the cones to their volumes are:
1) Cone 1 Volume: V = 32π in³
2) Cone 2 Volume: V = 60π in³
3)Cone 3 Volume: V = 100π/3 in³
What is the Volume of the cone?
1) We are given:
base area = 16π in²
height = 6 in
Base is a circle and as such formula for the base area is:
Base area = πr²
Thus:
16π = πr²
r = 4 in
Formula for volume is:
V = ¹/₃ × πr²h
Thus:
V = ¹/₃ × π(4)² × (6)
V = 32π in³
2) The dimensions of the cone are:
diameter = 12 in
Thus; r = 12/2 = 6 in
Height: h = 5 in
Thus:
V = ¹/₃ × π(6)² × (5)
v = 60π in³
3) The dimensions of the cone are:
r = 5 in
Height: h = 4 in
Thus:
V = ¹/₃ × π(5)² × (4)
V = 100π/3 in³