Question

A hemispherical piece of metal of radius 42 cm is melted and part of this melted metal is utilised to make 4 cone of radius 20cm and height 21cm each .3608 cm^3 of metal is wasted .The remaining metal is used to make spherical balls of radius 21 cm Find the number of balls that can be made



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Answer 1

Answer:

3 balls

Step-by-step explanation:

Radius of hemisphere = 42 cm

Vol. of hemisphere = $\frac{2}{3} \pi$$r^{3}$

= 2/3 x 22/7 x 42 x 42 x 42

= 155232 cm cube

Vol. of 4 cones = 4 x $\frac{1}{3} \pi r^{2} h$

= 4 x 1/3 x 22/7 x 20 x 20 x 21

= 8800 x 4

= 35200 cm cube

Vol. remaining = 155232 - 35200 - 3608 (wasted)

= 116242 cm cube

Vol. of balls = $\frac{4}{3} \pi r^{3}$

= 4/3 x 22/7 x 21 x 21 x 21

= 88 x 21 x 21

= 38808 cm cube

No. of balls = 116424 / 38808

= 3 balls