A solid sphere of radius 3cm is melted and
reformed by stretching it into a cylindrical
shaped wire of length 9cm. Find the radius of
the wire
Answers
Step-by-step explanation:
Given:-
A solid sphere of radius 3cm is melted and
reformed by stretching it into a cylindrical
shaped wire of length 9cm.
To find:-
Find the radius of the wire?
Solution:-
Radius of the solid sphere =(r)=3 cm
Length of the cylindrical shaped wire after reformed = 9cm
Height of the cylindrical wire (h)=9cm
If one solid is converted into another solid then the volume of both solids remain same.
Volume of a sphere = 4/3 πr^3 cubic units
=>V= (4/3)×(22/7)×(3)^3 cubic cm
=>V = (4×22×27)/(3×7) cm^3
=>V= 4×22×9/7 cm^3
=>V= 792/7 cm^3
Volume of the spherical solid = 792/7 cm^3 ---(1)
Volume of the cylinder = πr^2 h cubic units
=>V = (22/7)×r^2×9 cubic cm
=>V= (22×9×r^2)/7 cm^3
=>V= 198r^2/7 cm^3
Volume of the cylindrical solid = 198r^2/7 cm^3-(2)
we know that
If one solid is converted into another solid then the volume of both solids remain same.
(1)=(2)
=>792/7 = 198r^2/7
=>792 = 198r^2
=>r^2 = 792/198
=>r^2 = 72/18
=>r^2 = 4
=>r^2 = 2^2
=>r = 2 cm
Radius = 2 cm
Answer:-
The radius of the wire for the given problem is 2cm
Used formulae:-
- If one solid is converted into another solid then the volume of both solids remain same.
- Volume of the cylinder = πr^2 h cubic units
Where , r = radius and h=height and π=22/7
- Volume of a sphere = 4/3 πr^3 cubic units
Where, r=radius and π=22/7
Step-by-step explanation:
RADIUS of sphere = 3cm
LENGTH of wire = 9cm
So , height (h) = 9cm
IF IT IS REFORMED AND MELTED INTO CYLINDRICAL SHAPED WIRE THEN,
VOLUME OF SPHERE = VOLUME OF CYLINDER
4/3 pie r³ = pie r²h
here, pie and pie gets canceled
4/3 ×3 ×3 ×3 = r² ×9
4 × 9 = r² × 9
4×9/9 = r²
4 = r²
or
r² =4
r = √4
r = 2
hence, the radius of sphere is 2cm
Done by Ayesha