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Home » A solid piece of iron in the form of a cuboid of dimensions 49cm × 33cm × 24cm, is moulded to form a solid sphere. The radius of the sphere is (A) 21cm (B) 23cm (C) 25cm (D) 19cm
A solid piece of iron in the form of a cuboid of dimensions 49cm × 33cm × 24cm, is moulded to form a solid sphere. The radius of the sphere is (A) 21cm (B) 23cm (C) 25cm (D) 19cm
CBSE | Class 10 | Exercise 12.1 | Maths | NCERT Exemplar | Surface Areas And Volumes
A solid piece of iron in the form of a cuboid of dimensions 49cm × 33cm × 24cm, is moulded to form a solid sphere. The radius of the sphere is (A) 21cm (B) 23cm (C) 25cm (D) 19cm

(A) 21cm

As we probably are aware,

Volume of cuboid = lbh

Where, l = length, b = broadness and h = tallness

For given cuboid,

Length, l = 49 cm

Broadness, b = 33 cm

Tallness, h = 24 cm

Volume of solid shape

    \[=\text{ }49\times \text{ }\left( 33 \right)\text{ }\times \text{ }\left( 24 \right)\text{ }cm3\]

Presently,

Leave the range of 3D square alone r.

As volume of circle

    \[=\text{ }4/3\text{ }\pi r3\]

Where r = range of circle

Too,

Volume of cuboid = volume of circle formed

Along these lines,

    \[49\left( 33 \right)\left( 24 \right)\text{ }=\text{ }4/3\text{ }\pi r3\]

    \[\Rightarrow \pi r3\text{ }=\text{ }29106\]

    \[\Rightarrow r3\text{ }=\text{ }29106\times 22/7\]

    \[\Rightarrow r3\text{ }=\text{ }9261\]

    \[\Rightarrow r\text{ }=9261\text{ }cm\text{ }=\text{ }21\text{ }cm\]

Consequently, sweep of circle is 21 cm

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