A semicircular sheet of diameter 28 cm is bent to form an openconical

1.	A semicircular sheet of diameter 28 cm is bent to form an openconical cup. Find the capacity of the cup. (Use sqrt 3 1.732.)
Answer» diameter =d = 28 cmRadius= r = 14 cmCircumference of semi circle = πr= (22/7) x 14 = 44 cm so the circumference of base of cone2πR = 44R = 44 x (7/44)R = 7 cm The radius of semi circular sheet = slant height of conical cupwhich isl = 7 cmAs,r2+ h2= l2 142+ h2= 72 196 – 49 = h2 h2= 147 hence; h = 7√3 cm depth of the conical cup= 7√3 cm Capacity of cup = (1/3)πr2h = (1/3) x (22/7) x 72x 7√3 = 622.37 cu cm approx

A semicircular sheet of diameter 28 cm is bent to form an openconical cup. Find the capacity of the cup. (Use sqrt 3 1.732.)

Answer»

diameter =d = 28 cmRadius= r = 14 cmCircumference of semi circle = πr= (22/7) x 14 = 44 cm

so the circumference of base of cone2πR = 44R = 44 x (7/44)R = 7 cm

The radius of semi circular sheet = slant height of conical cupwhich isl = 7 cmAs,r2+ h2= l2

142+ h2= 72

196 – 49 = h2

h2= 147

hence; h = 7√3 cm

depth of the conical cup= 7√3 cm

Capacity of cup = (1/3)πr2h

= (1/3) x (22/7) x 72x 7√3

= 622.37 cu cm approx