A semi circular sheet of diameter 28 cm is bent into an open conical cup . Find the depth and capacity of cup .
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radius of circle = d/2 = 28/2= 14 cm.
r=l.
l=14cm.
circumference of circle of diameter 28cm = 2*π*(14)= 2*22/7*14= 88cm.
circumference of base circle of cone(1/2*circumference of circle) = 1/2*88cm=44cm.
circumference of base circle =2*π*r=44cm.
r=7cm(radius of base circle).
By pythagoras theorem:-
hyp^2= b^2+p^2.
l^2=r^2+h^2.
14^2=7^2+h^2.
196=49+h^2.
h= 12.12....
Therefore,depth of the cone= 12.12cm.
capacity =volume= 1/3*π*r^2*h=
1/3*22/7*(7)^2*12.12=622.16cm^3
r=l.
l=14cm.
circumference of circle of diameter 28cm = 2*π*(14)= 2*22/7*14= 88cm.
circumference of base circle of cone(1/2*circumference of circle) = 1/2*88cm=44cm.
circumference of base circle =2*π*r=44cm.
r=7cm(radius of base circle).
By pythagoras theorem:-
hyp^2= b^2+p^2.
l^2=r^2+h^2.
14^2=7^2+h^2.
196=49+h^2.
h= 12.12....
Therefore,depth of the cone= 12.12cm.
capacity =volume= 1/3*π*r^2*h=
1/3*22/7*(7)^2*12.12=622.16cm^3
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