Question

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??​

Answer 1

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

Answer 2

★ 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:

→ $\sf{\boxed{Volume\:of\:cuboid=lbh}}$

→ $\sf{\boxed{Volume\:of\:sphere=\dfrac{4}{3}\pi\:r^3}}$

★ 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:

$\sf{=\dfrac{4}{3}\times\dfrac{22}{7}\times\:r^3=38808\:cm^3}$

→ Moving the constants to the RHS:

$\sf{r^3=38808\times\dfrac{3}{4}\times\dfrac{7}{22}}$

$\sf{r^3=9261}$

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