Question

A metal hemisphere of radius 30 mm is drawn into a wire of 12 mm diameter. Find the length
of the wire [mm = millimetre) ]
a .300 mm
b. 400 mm
c.500 mm
d. 600 mm​

Answer 1

Answer:

2/3 π 30^3 = π144h

180π=π144h

180 =144 h

h=1.25

Answer 2

Answer:

The length of the wire is 500mm.

Step-by-step explanation:

• The radius of metal hemesphere is =r=30mm
• The diameter of the wire is=d=12 mm
• The radius of the wire will be=R= d/2=12/2=6mm
• According to question,
• A metal hemisphere of radius 30 mm is drawn into a wire of 12 mm diameter.
• That means, the volume of the hemesphere=the volume of the wire.
• The volume of the hemesphere= 2/3×π×(radius)²
• =2/3×π×(r)²
• The volume of the wire =π×(R)²×h
• where ,h is the length of the wire.
• So, 2/3×π×(r)³=π×(R)²×h
• putting the values of r and R, we get
• 2/3×π×(30)³=π×6²×h
• 2/3×π×(30)³=π×6²×h(2/3)×30×30×30=36×h
• 2/3×π×(30)³=π×6²×h(2/3)×30×30×30=36×h36h=18000
• 2/3×π×(30)³=π×6²×h(2/3)×30×30×30=36×h36h=18000h=18000/36
• h=500mm

Conclusion:

The length of the wire is found to be 500mm