Question

a semicircular sheet of diameter 28cm is bent to make a cone find the volume of the cone​

Answer 1

Solution:-
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
Answer.

Answer 2

Solution :-

Given :

A semicircular sheet of diameter 28 cm is bent to make a cone.

Radius = r = 28/2 = 14 cm

Circumference of semicircle = 14π = 44 cm

When we bent the semicircular sheet into a cone then the slant height cone will be equal to the radius of semicircle.

Circumference of the base of the cone = Circumference of the semicircle = 2πr

=> 44 = 2πr

=> r = (44 × 7)/(22 × 2) = 7

Height of cone = h = √(l² - r²)

= √(14² - 7²)

= √(196 - 49)

= √147

We know that,

Volume of cone = ⅓πR²h cu. units

Volume of cone = ⅓ × 22/7 × (7)² × √147 cm³

= (1078√3)/3 cm³

Hence,

Volume of cone = (1078√3)/3 cm³ or 622.38 cm³