A semicircular thin sheet of metal of diameter 28cm is bent to make an open conical cup find the capacity of the cup . plz answer .
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Answered by
50
radius o the thin sheet = 28/2 = 14
lenghth of semicircular thin sheet = 2 pie r/2 = pie r
= 22/7 * 14
= 44 cm
semicircular thin sheet is turned into the circumference of base of cone with slant height 14cm .
circumference = 2pie r
44= 2 * 22 / 7 * r
r = 44 * 7 / 2 * 22 = 7cm
h = sqrt{ L^2 - r'^2}
= sqrt { 14^2 * 7^2 }
= sqrt { 196 - 49 }
= sqrt { 147 }
= sqrt { 7 * 7 *3 }
= 7 sqrt { 3 }
vol. of cone = 1/3 pie r'^2 h
= 1/3 * 22/7 * 7^2 * 7 sqrt { 3 }
= 1078 * 1.732 / 3
= 622.3653 cm^3
lenghth of semicircular thin sheet = 2 pie r/2 = pie r
= 22/7 * 14
= 44 cm
semicircular thin sheet is turned into the circumference of base of cone with slant height 14cm .
circumference = 2pie r
44= 2 * 22 / 7 * r
r = 44 * 7 / 2 * 22 = 7cm
h = sqrt{ L^2 - r'^2}
= sqrt { 14^2 * 7^2 }
= sqrt { 196 - 49 }
= sqrt { 147 }
= sqrt { 7 * 7 *3 }
= 7 sqrt { 3 }
vol. of cone = 1/3 pie r'^2 h
= 1/3 * 22/7 * 7^2 * 7 sqrt { 3 }
= 1078 * 1.732 / 3
= 622.3653 cm^3
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24
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