Question

areas of three adjacent faces of a cuboid are 11cm², 20cm² and 55cm² respectively. the cuboid is melted and recast into spheres each of radius 0.5cm. Find the number of spheres, so obtained?

Answer 1

Answer:

140.12

Step-by-step explanation:

Let the three sides be x, y and z.

so

ATQ,

xy=11 ------1

yz=20----------2

zx=55----------3

Multiplying 1,2 and 3, we get,

xy*yz*zx=11*20*55

x²y²z²=12100

squaring on both sides we get,

xyz=110

thus, volume of the cuboid is 110 cm³.

now, volume of sphere=$\pi$r²

so if r=0.5

then,

volume= 3.14 × 0.5 × 0.5

=0.785 cm³

So, number of spheres formed=$\frac{volume of cuboid}{volume of 1 sphere}$

=$\frac{110}{0.785}$

=140.12