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▶Two cones with same base radius 7cm are inserted one in another.Find the volume of air in between the two cones if the vertical cross-section of their combination is as shown in the diagram. /_BDC = 120 and /_BAC = 60.
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In triangle COA
<OAC = 60/2 = 30
tan30 = OC/OA
OA = OC/tan30
= 7√3
In triangle ODC
<ODC = 120/2 = 60
tan 60 = OC/OD
OD = OC/tan 60
= 7/√3
volume of cone BAC = 1/3 pie r^2 h
r = 7
h = OA = 7√3
V= 1/3 22/7 7× 7 × 7√3
= 610.86 cm^3
volume of BDC = 1/3 pie r^2 h
r = 7
h = OD = 7/√3
V = 1/3 ×22/7 × 7× 7 × 7/√3
= 211.18 cm^3
volume of air between cones = volume of BAC - Volume of BDC
= 610.86 - 211.18
= 399.68 cm^3
<OAC = 60/2 = 30
tan30 = OC/OA
OA = OC/tan30
= 7√3
In triangle ODC
<ODC = 120/2 = 60
tan 60 = OC/OD
OD = OC/tan 60
= 7/√3
volume of cone BAC = 1/3 pie r^2 h
r = 7
h = OA = 7√3
V= 1/3 22/7 7× 7 × 7√3
= 610.86 cm^3
volume of BDC = 1/3 pie r^2 h
r = 7
h = OD = 7/√3
V = 1/3 ×22/7 × 7× 7 × 7/√3
= 211.18 cm^3
volume of air between cones = volume of BAC - Volume of BDC
= 610.86 - 211.18
= 399.68 cm^3
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