An iron spherical ball of volume 232848 cm³ has been melted and converted into a cone with the vertical angle of 120º. What are its height and base?
Answers
Dear Student,
Answer: Height of cone = 42 cm
radius (r) of cone = 72.74 cm
Solution:
Let the radius of the cone is r, and height of cone is h.
Vertical angle is 120°, height divides this angle into half, 60°
tan 60° = perpendicular/base = r/h
√3 = r/h ∵ tan 60°= √3
r = √3 h or h = r/√3
Volume of cone = 1/3 π r² h
since the same amount of iron is used to make the cone
1/3 π r² h = 232848
To calulate r:
put h = r/√3
1/3 π r²(r/√3) = 232848
r³ =( 232848×3×√3 )/π
r³ =( 232848×3×√3×7 )/22
r³ = 8469395.89/22 = 384972.54
radius (r) of cone = 72.74 cm
Base diameter = 2 × 72.74 = 145.49 cm
Base area = πr² = 3.14 ×(72.74)²
base area = 3.14 ×5291.1 = 16614 cm² = 1.6 m²
To calculate h:
put r = √3 h
1/3 π (√3 h)² h = 232848
1/3 π×3×h³ = 232848
h³ = 232848×7/22
h = ∛74088
h = 42 cm
Height of cone = 42 cm.
Hope it helps you.
Answer:
Answer : the height of cone is 42 cm