Question

10. A semicircular sheet of metal of diameter 28 cm
is bent into an open conical cup. Find the depth
and capacity of cup. (V3 = 1.73) (HOTS)​

Answer 1

Slant height of the conical cup, 'l' = radius of the semi-circular sheet, R = 14 cm

Let radius and height of the conical cup be 'r' and 'h' respectively.

Circumference of the base of the cone = Length of arc of the semi-circle

Or, 2πr = (1/2)2πR

Or, 2πr = (1/2)(2π)(14)

Or, r = 7 cm

Now, we know that l² = h² + r²

(14)² = (h)² + (7)²

h² = 196 - 49

h = √147

Height or depth of the conical cup = 12.124 cm

Now, capacity of the conical cup = 1/3πr²h

= 1/3*22/7*7*7*12.124

= 13069.672/21

Capacity of the conical cup = 622.365 cu cm