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# 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

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