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प्रश्न
A solid piece of iron in the form of a cuboid of dimensions 49 cm × 33 cm × 24 cm, is moulded to form a solid sphere. The radius of the sphere is ______.
पर्याय
21 cm
23 cm
25 cm
19 cm
उत्तर
A solid piece of iron in the form of a cuboid of dimensions 49 cm × 33 cm × 24 cm, is moulded to form a solid sphere. The radius of the sphere is 21 cm.
Explanation:
As we know,
Volume of cuboid = lbh
Where, l = length, b = breadth and h = height
For given cuboid,
Length, l = 49 cm
Breadth, b = 33 cm
Height, h = 24 cm
Volume of cube = 49 × (33) × (24) cm3
Now,
Let the radius of cube be r.
As volume of sphere = `4/3 pir^3`
Where r = radius of sphere
Also, volume of cuboid = volume of sphere molded
So, 49(33)(24) = `4/3 pir^3`
⇒ πr3 = 29106
⇒ r3 = `29106 xx 22/7`
⇒ r3 = 9261
⇒ r = `root(3)(9261)` cm = 21 cm
Hence, radius of sphere is 21 cm
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