Question

twelve solid sphere of the same size are made by melting a solid metallic cylinder of base diameter 2cm and height 16cm. the diameter of each sphere is what
a)4cm b) 3cm c)2cm d) 6cm​

Answer 1

HeYa❤️...

Answer:

Correct option : c) 2cm

Explanation:

→Solid cylinder is recasted into 12 spheres.

→So, the volume of 12 spheres will be equal to the volume of cylinder.

12 For spheres

R=?

For Cylinder

r=2/2 = 1cm

h=16cm.

Volume of 12 spheres = Volume of cylinder

$= > \: \frac{4}{3\pi \: r {}^{3} } = \pi \: r {}^{2} h \\ \\ = > \: r = \frac{3r {}^{2}h }{4 \times 12} = \frac{3 \times 1 \times 1 \times 16}{4 \times 12} \\ \\ = > \: r = 1cm .$

Hence, diameter = 2r = 2(1) = 2cm.

I hOpe It HeLpS Ya!

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Answer 2

Radius of cylinder (R) = 1cm

Height of cylinder (H) = 16cm

Let, the radius of small spheres be rcm

So,

12(volume of small sphere) = volume of cylinder

=> 12(4/3πr^3) = πR^2H

=> 16r^3 = 1^2 × 16

=> r^3 = 1cm

=> r = 1cm.