A solid iron cuboid of dimensions 49 cm × 33 cm × 24 cm is melted to form a solid sphere, then its radius is (A) 21 cm
A solid iron cuboid of dimensions 49 cm × 33 cm × 24 cm is melted to form a solid sphere, then its radius is
(A) 21 cm
(B) 13 cm
(C) 24 cm
(D) 18 cm
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Correct option is: (A) 21 cm
Dimensions of cuboid are 49 cm \(\times\) 33 cm \(\times\) 24 cm.
Let the radius of sphere be r cm.
\(\because\) Solid iron cuboid is melted to form a solid sphere.
\(\therefore\) Volume of sphere = volume of cuboid
= \(\frac 43\pi r^3\) = 49 \(\times\) 33 \(\times\) 24
= \(r^3 = \frac {49 \times 33 \times 24 \times 3 \times 7}{4\times22} = 7^3 \times 3^3 = 21^3\)
\(\therefore\) r = 21
Hence, the radius of the formed solid sphere is 21 cm
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