Question

A semi-circular thin sheet of the metal of diameter 28 cm is bent and an open conical cup of the largest size is made. Find the capacity (volume ) of the cup . (√3=1.732

Answer 1

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Answer 2

Answer:

The capacity of the cup is 622.16 centimeter cube.  

Step-by-step explanation:

Given : A semi-circular thin sheet of the metal of diameter 28 cm is bent and an open conical cup of the largest size is made.

To Find : The capacity (volume ) of the cup?

Solution :

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

Let slant height of the conical cup be l = radius of the semi-circular sheet be R.

So, R=l=14 cm

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

i.e. $2\pi r=\frac{1}{2}\times 2\pi R$

$r=\frac{1}{2}R$

$r=\frac{1}{2}\times 14$

$r=7$

The height of the conical cup is

$h=\sqrt{l^2-r^2}$

$h=\sqrt{14^2-7^2}$

$h=\sqrt{196-49}$

$h=\sqrt{147}$

$h=12.12$

The volume of the conical cup is

$V=\frac{1}{3}\pi r^2 h$

$V=\frac{1}{3}\times \frac{22}{7}\times 7^2\times 12.12$

$V=622.16$

Therefore, The capacity of the cup is 622.16 centimeter cube.