14. A semi circular sheet of metal of diameter 28 cmis bent into an op

1.	14. A semi circular sheet of metal of diameter 28 cmis bent into an open conical cup. Find the depth andIT-II (2011)]capacity of the cup.
Answer» Given: Diameter = 28 cm Radius, r = 14 cm Circumference of semi circle = πr= (22/7) x 14 = 44 cm This becomes circumference of base of cone2πR = 44R = 44 x (7/44)R = 7 cm The radius of semi circular sheet = slant height of conical cupThat is l = 7 cm We know that r2+ h2= l2142+ h2= 72196 – 49 = h2h2= 147 Therefore, h = 7√3 cm That is depth of the conical cup is 7√3 cm Capacity of cup = (1/3)πr2h = (1/3) x (22/7) x 72x 7√3 = 622.37 cu cm

14. A semi circular sheet of metal of diameter 28 cmis bent into an open conical cup. Find the depth andIT-II (2011)]capacity of the cup.

Answer»

Given:

Diameter = 28 cm

Radius, r = 14 cm

Circumference of semi circle = πr= (22/7) x 14 = 44 cm

This becomes circumference of base of cone2πR = 44R = 44 x (7/44)R = 7 cm

The radius of semi circular sheet = slant height of conical cupThat is l = 7 cm

We know that r2+ h2= l2142+ h2= 72196 – 49 = h2h2= 147

Therefore, h = 7√3 cm

That is depth of the conical cup is 7√3 cm

Capacity of cup = (1/3)πr2h

= (1/3) x (22/7) x 72x 7√3

= 622.37 cu cm