A semi-circular sheet of metal of diameter 28cm is bent to form an open conical cup. Find the capacity of the cup.
Solution:
Given, a semi-circular sheet of metal is bent to form a open conical cup
The diameter of metal sheet is 28 cm
We have to find the volume of the cup.
Circumference of base of cone = circumference of semicircle
Let the radius of cup be R.
Circumference of base of cone = 2πR
Diameter of semicircle = 28 cm
So, radius = 28/2 = 14 cm
Circumference of semicircle = πr
Where, r is the radius of semicircle
= π(14)
= 14π
Now, 2πR = 14π
2R = 14
R = 14/2
R = 7 cm
Volume of cone = 1/3 πr²h
Where, r is the radius of cone
h is the height of cone
Slant height of the cone = radius of semicircle = 14 cm
We know, l² = r² + h²
(14)²= (7)² + h²
196 = 49 + h²
h² = 196 - 49
h² = 147
Taking square root,
h = 7√3 cm
Volume of cup = 1/3 (22/7)(7)²(7√3)
= 22(49)(√3)/3
= 1867.096/3
= 622.37 cm³
Therefore, the volume of the cup is 622.37 cm³
✦ Try This: A semi-circular sheet of metal of diameter 24 cm is bent to form an open conical cup. Find the capacity of the cup.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 13
NCERT Exemplar Class 9 Maths Exercise 13.4 Problem 2
A semi-circular sheet of metal of diameter 28cm is bent to form an open conical cup. Find the capacity of the cup.
Summary:
A semi-circular sheet of metal of diameter 28cm is bent to form an open conical cup. The capacity of the cup is 622.37 cm³
☛ Related Questions:
- A cloth having an area of 165 m² is shaped into the form of a conical tent of radius 5 m. How many s . . . .
- A cloth having an area of 165 m² is shaped into the form of a conical tent of radius 5 m. Find the v . . . .
- The water for a factory is stored in a hemispherical tank whose internal diameter is 14 m. The tank . . . .