Question

diameter of the sphere....??

Answer 1

Here, Two metallic circular cones are melted and recast into a sphere.

So, Volume of two cone + Volume of Cone 2 = Volume of Sphere ----- (1)

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Given, Height of cone 1 = 4.1 cm.

Given, Height of cone 2 = 4.3 cm.

Given, Radius r = 2.1

We know that Volume of cone = $(\frac{1}{3})\pi r^2h$

$= > (\frac{1}{3}) * \pi * (2.1)^2 * 4.1 + (\frac{1}{3}) * \pi * (2.1)^2 * 4.3$

$= > (\frac{1}{3}) * \pi * (2.1)^2 * (4.1 + 4.3)$

$= > (\frac{1}{3}) * \pi * (2.1)^2 * 8.4$

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We know that volume of sphere = $\frac{4}{3} \pi R^3$

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Substitute both the equations in (1), we get

$= > \frac{1}{3} * \pi * (2.1)^2 * 8.4 = \frac{4}{3} * \pi * R^3$

$= > (2.1)^2 * 2.1 * 4 = 4R^3$

$= > (2.1)^3 * 4 = R^3 * 4$

Both the sides are equal.

= > R = (2.1).

We know that Diameter = 2R = 4.2cm.

Therefore, Diameter of the sphere = 4.2cm.

Hope this helps!