Question

A solid pieces of iron the form of a cuboid of dimention 49cm x 33cm x 24cm is moulded to form a solid sphere . radious of the sphere is

Answer 1

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Answer 2

Given :-

Length of the cuboid = 49 cm

Breadth of the cuboid = 33 cm

Height of the cuboid = 24 cm

To Find :-

The radius of the sphere.

Solution :-

We know that,

• l = Length
• b = Breadth
• h = Height
• r = Radius

Given that,

Length (l) = 49 cm

Breadth (b) = 33 cm

Height (h) = 24 cm

$\underline{\boxed{\sf Volume \ of \ cuboid = lbh }}$

Substituting their values, we get

Volume of cube = $\sf 49 \times (33) \times (24) \ cm^{3}$

According to the question,

Let the radius of cube be r.

As volume of sphere = $\sf \dfrac{4}{3} \pi r^{3}$

Where r = radius of sphere

$\underline{\boxed{\sf Volume \ of \ cuboid = Volume \ of \ sphere \ molded }}$

Substituting their values, we get

$\sf 49(33)(24) = \dfrac{4}{3} \pi r^{3}$

$\implies \sf \pi r^{3}=29106$

$\implies \sf r^{3} = 29106 \times \dfrac{22}{7}$

$\implies \sf r^{3} = 9261$

$\implies \sf r = \sqrt{ 9261} \ cm = 21 \ cm$

Therefore, radius of sphere is 21 cm