Question

a semicircular sheet of metal of diameter 28 cm is bent into an open conical cup . find the depth and capacity of cup

Answer 1

Yes, you use the formula for a cone volume to find the capacity.

depth = √147≈12.1cm

capacity ≈622cm3

Explanation:

C=2⋅π⋅r and V=13⋅π⋅r22⋅h

Diameter=28cm,→r1=14cm

From the semicircular piece of metal we first find the circumference of the base of the cone, which is the same as ½ of the full circle,
C=2⋅π⋅r12
C=2⋅π⋅142=14π≈44cm

Now find our cone radius from the cone circumference.

C=2⋅π⋅r2→ r2=(C2⋅π)

r2=14π2⋅π=7

From Pythagoras, the equation for a right triangle

r21=r22+h2 we obtain:

h=√r21–r22 → h=√196–49

h=√147(≈12.1cm  this is the depth of the cone cup)

V=13⋅π⋅r22⋅h

V=13⋅π⋅49⋅√147

V=622cm3 volume capacity