Answer: 1) V = 37.68 [tex]ft^{3}[/tex]
2) V= 301.44 [tex]cm ^{3}[/tex] (Equal volumes)
Step-by-step explanation:
1) Total volume of all 3 cones = 3v, where (V) is volume for 1 cone.
Right circular cone: line segment from point to center base = height
line segment from center base to circumference (circle) = radius
V = [tex]\frac{1}{3}[/tex] b * h b = [tex]\pi r^{2}[/tex] (r ) = 2ft ([tex]\pi[/tex])= 3.14 (h ) = 3ft
V = [tex]\frac{1}{3}[/tex] ( [tex]\pi r ^{2}[/tex] ) * 3
V = [tex]\frac{1}{3}[/tex] (3.14)( [tex]2^{2}[/tex] ) * 3
V = [tex]\frac{1}{3}[/tex] (3.14) (4) * 3
V = (1 )(3.14)(12) ÷ 3
V = 37.68 ÷ 3
V = 12.56 [tex]ft ^{3}[/tex] then for total of all 3: 12.56 * 3 = 37.68 [tex]ft ^{3}[/tex] ( V = cubed unit)
2) Cone: V = [tex]\frac{1}{3}[/tex] b * h = { [tex]\frac{1}{3}[/tex] ([tex]\pi[/tex]) ([tex]6^{2}[/tex] ) (8) } = { (3.14) (36) (8) ÷ 3 } = { 904.32 ÷ 3 } =
V = 301.44 [tex]cm ^{3}[/tex]
Cylinder: V= [tex]\pi r ^{2}[/tex] h = {(3.14) ([tex]4 ^{2}[/tex] ) (6)} = { 3.14 * 16 * 6)=
V = 301.44 [tex]cm ^{3}[/tex]
