A solid piece of iron in the form of a cuboid of dimensions 49cm × 44cm × 18cm, is moulded to form a solid sphere. The radius of the sphere is??
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A solid piece of iron in the form of a cuboid of dimensions 49cm × 44cm × 18cm, is moulded to form a solid sphere. The radius of the sphere is??
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★ Given:
A solid piece of iron in the form of a cuboid of dimensions 49cm × 44cm × 18cm, is moulded to form a solid sphere.
★ To Find:
The radius of the sphere.
★ Formulae to be used:
→
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★ Solution:
Length of the cuboid = 49 cm
Breadth = 44 cm
Height = 18 cm
Volume of the cuboid = lbh
= 49 x 44 x 18
= 38808 cm³
As the same solid iron is remoulded to form a sphere, the volume of the sphere will be also the same.
Formula to find the volume of sphere = 4/3πr³ ----- (1)
Given volume = 38808 cm³ ----- (2)
Combining (1) and (2):
4/3πr³ = 38808 cm³
→ Giving the value of π as 22/7:
→ Moving the constants to the RHS:
So,
r = ∛9261
r = 21 cm
Hence, the radius of the sphere is 21 cm.
Knowledge Bytes:
✳ Volume of cube = a³
✳ Volume of cuboid = lbh
✳ Volume of sphere = 4/3πr³
✳ Volume of cylinder = πr²h
✳ Volume of cone = 1/3πrh
Verified answer
Answer:
volumes are always same for both cuboid and sphere so lbh=49×4×18=38808 . now for sphere volume =4/3pi r square.so from this equation we get radius to be 21cm