Question

how many solid sphere each 12 cm in diameter could be moulded from a solid metal cylinder of height 10 cm and 24 cm? cive me answer

Answer 1

30 solid sphere each 12 cm in diameter could be moulded from a solid metal cylinder of height 10 cm and diameter 24 cm.

Step-by-step explanation:

The diameter of solid sphere = 12 cm

Radius of the solid sphere r = 6 cm

We know that volume of solid sphere is given by

$V=\frac{4}{3}\pi r^3$

Therefore, the volume of the solid sphere

$V=\frac{4}{3}\pi\times 6\times 6$

$\implies V=48\pi$

Given

Height of the cylinder h = 10 cm

Diameter of cylinder = 24 cm

Radius of the cylinder R = 12 cm

Volume of the solid cylinder is given by

$V'=\pi R^2h$

$\implies V'=\pi\times 12\times 12\times 10$

$\implies V'=1440\pi$

Thus, the number of solid spheres that can be made from the cylinder

$=\frac{V'}{V}$

$=\frac{1440\pi}{48\pi}$

$=30$

Therefore, 30 solid spheres could be moulded from the solid metal sphere.

Hope this answer is helpful.

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