Question

a m a metallic sphere of radius 4.2 is melted and recast into the shape of a cylinder of radius 6 cm find the height of the cylinder

Answer 1

Answer: h= 2.744 cm

Step-by-step explanation:

Volume of sphere = Volume of cylinder

4/3 × 22/7 ×42/10 ×42/10 ×42/10 = 22/7 ×6×6×h

h = 4/10×14×7/10×7/10

= 2744/1000

= 2.744 cm

Answer 2

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Here,

Radius of cylinder, r = 6cm

Height of cylinder, h = ?

Radius of sphere, r' = 4.2cm

Now,

Volume of cylinder = Volume of sphere

$\implies\tt\pi {r}^{2} h = \frac{4}{3} \pi {r'}^{3}$

$\implies\tt {6}^{2} \times h = \frac{4}{3} \times {(4.2)}^{3}$

$\implies\tt 36h = \frac{4}{3} \times 4.2 \times 4.2 \times 4.2$

$\implies\tt 36h = 4 \times 1.4 \times 4.2 \times 4.2$

$\implies\tt h = \frac{5.6 \times 17.64}{36}$

$\implies\tt h = 5.6 \times 0.49$

$\implies\tt h = 2.744 \: cm$

Thus, height of the cylinder is 2.744cm