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 R2πr=
2
1
×2πR
r=\frac{1}{2}Rr=
R
r=\frac{1}{2}\times 14r=
×14
r=7r=7
The height of the conical cup is
h=\sqrt{l^2-r^2}h=
l
−r
h=\sqrt{14^2-7^2}h=
14
−7
h=\sqrt{196-49}h=
196−49
h=\sqrt{147}h=
147
h=12.12h=12.12
The volume of the conical cup is
V=\frac{1}{3}\pi r^2 hV=
3
πr
h
V=\frac{1}{3}\times \frac{22}{7}\times 7^2\times 12.12V=
×
7
22
×7
×12.12
V=622.16V=622.16
Therefore, The capacity of the cup is 622.16 centimeter cube.
Answer:
Thanks u so much
bro
ur the best bro.....
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Answers & Comments
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 R2πr=
2
1
×2πR
r=\frac{1}{2}Rr=
2
1
R
r=\frac{1}{2}\times 14r=
2
1
×14
r=7r=7
The height of the conical cup is
h=\sqrt{l^2-r^2}h=
l
2
−r
2
h=\sqrt{14^2-7^2}h=
14
2
−7
2
h=\sqrt{196-49}h=
196−49
h=\sqrt{147}h=
147
h=12.12h=12.12
The volume of the conical cup is
V=\frac{1}{3}\pi r^2 hV=
3
1
πr
2
h
V=\frac{1}{3}\times \frac{22}{7}\times 7^2\times 12.12V=
3
1
×
7
22
×7
2
×12.12
V=622.16V=622.16
Therefore, The capacity of the cup is 622.16 centimeter cube.
Answer:
Thanks u so much
bro
ur the best bro.....