Question

a solid metallic cone is 24 cm high and radius of its base is 6 cm.If it is melted and recast into a solid sphere,find the radius of the sphere?​

Answer 1

EXPLANATION.

height of solid metallic cone = 24 cm.

radius of solid metallic cone = 6 cm.

it recast into a solid sphere.

TO find the radius of the sphere.

volume of solid sphere = 4/3πr³.

volume of solid metallic cone = 1/3πr²h.

Volume of solid sphere = volume of cone

= 4/3πR³ = 1/3πr²h

= 4πR³ = πr²h

= 4R³ = r²h

= R³ = 6 X 6 X 24 / 4

= R³ = 6 X 6 X 6

= R³ = 216 cm.

More information.

= volume of cylinder = πr²h

= volume of cone = 1/3πr²h

= volume of sphere = 4/3πr³

= volume of hemisphere = 2/3πr³

Answer 2

✯ Given :-

• A solid metallic cone is 24 cm height and radius of its base is 6 cm.

✯ To Find :-

• What is the radius of the sphere.

✯ Formula Used :-

$\boxed{\bold{\small{✬\: Volume\: of\: the\: solid\: sphere\: =\: Volume\: of\: the\: solid\: cone\: ✬}}}$

✯ Solution :-

» Let, the radius of the solid sphere be R.

» Height of the cone, h = 24 cm

» Base radius of the cone, r = 6 cm

➣ According to the question by using the formula we get,

$\boxed{\bold{\large{✮\: \dfrac{4}{3}πR³\: =\: \dfrac{1}{3}πr²h\: ✮}}}$

⇒ R³ = $\dfrac{r²h}{4}$

⇒ R³ = $\dfrac{6 × 6 × 24}{4}$

⇒ R³ = $\sf\dfrac{\cancel{864}}{\cancel{4}}$

➥ R³ = 216 cm

$\therefore$ The radius of the sphere is ${\boxed{\underline{\underline{\bf{216\: cm}}}}}$

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