Question

a metallic sphere of radius 4.2 cm is melted and recast into a shape of cone of radius 6 centimetre find the height of the cone​

Answer 1

Answer:

• Height of the cone = 8.23 cm.

Explanation:

Let radius of sphere be 'r' and radius of cone be 'R'.

Given:

• Radius of metallic sphere (r) = 4.2 cm
• Radius of cone (R) = 6 cm

To Find:

• Height of cone.

Now, we know that:

$\longrightarrow \sf Volume\;of\;sphere = \dfrac{4}{3}\pi r^{3} \\ \\ \longrightarrow Volume\;of\;cone=\dfrac{1}{3}\pi R^{2}h$

Now, sphere is recant in a cone but the volume remains same.

$\therefore \sf Volume\;of\;sphere=Volume\;of\;cone\\ \\ \longrightarrow \sf \dfrac{4}{3}\pi r^{3}=\dfrac{1}{3}\pi R^{2}h \\ \\ \\ \longrightarrow \sf \dfrac{4}{3} \times \pi \times 4.2\times 4.2\times 4.2=\dfrac{1}{3}\times \pi \times 6\times 6\times h\\ \\ \\ \longrightarrow \sf h = \dfrac{4\times 4.2\times 4.2\times 4.2\times 3}{3\times 6\times 6}\\ \\ \\ \longrightarrow \sf h = \dfrac{889.056}{108}\\ \\ \\ \longrightarrow \sf h = 8.23\;cm$

Hence, Height of the cone = 8.23 cm.

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