A solid metallic sphere of radius 4.2 cm is melted and recast into a right circular cylinder of radius 6 cm. What is the height (in cm) of the cylinder (correct to one decimal place)?
- A1.8
- B2.1
- C3
- D2.7
Solution & Step-by-step Explanation
When an object is melted and recast into another shape, its volume remains constant.
Volume of Sphere=Volume of Cylinder
3
4
πR
3
=πr
2
h
Where:
Radius of sphere, R=4.2cm
Radius of cylinder, r=6cm
Height of cylinder = h
3
4
×(4.2)
3
=6
2
×h
3
4
×4.2×4.2×4.2=36×h
4×1.4×4.2×4.2=36×h
5.6×17.64=36×h
98.784=36×h
h=
36
98.784
=2.744cm
Correct to one decimal place, the height is 2.7cm.
Volume of Sphere=Volume of Cylinder
3
4
πR
3
=πr
2
h
Where:
Radius of sphere, R=4.2cm
Radius of cylinder, r=6cm
Height of cylinder = h
3
4
×(4.2)
3
=6
2
×h
3
4
×4.2×4.2×4.2=36×h
4×1.4×4.2×4.2=36×h
5.6×17.64=36×h
98.784=36×h
h=
36
98.784
=2.744cm
Correct to one decimal place, the height is 2.7cm.