Question

a solid cone has the height of 10cm and diameter of 20 cm how many spheres of diameter 2cm can be made by melting it​

Answer 1

$\large\mathfrak \pink{Solution:-}$

$\underline \mathbb{GIVEN:-}$

➙Height of the solid cone = 10 cm .

➙Diameter of the solid cone = 20 cm.

So, Radius = 10 cm.

➙Diameter of the sphere = 2 cm.

So, Radius = 1 cm.

$\underline \mathbb{TO \: FIND:-}$

How many spheres can be formed.

$\underline \mathbb{FORMULA:-}$

Radius = 2 × Diameter

$Volume \: of \: the \: \: cone = \frac{1}{3} \pi \: r {}^{2} h$

$Volume \: of \: the \: sphere \: = \frac{4}{3} \pi \: {r}^{3}$

$\underline \mathbb{BY \: THE \: PROBLEM:-}$

$Volume \: of \: the \: cone = \frac{1}{3} \pi \: r {}^{2} h \\ \\ \implies \: \frac{1}{3} \pi \: (10) {}^{2} 10 \\ \\ \implies \: \frac{1}{3} \pi \: 1000\\ \\ \implies \frac{1000\pi}{3}$

$Volume \: of \: the \: sphere \: = \frac{4}{3} \pi \: {r}^{3} \\ \\ \implies \: \frac{4}{3} \pi \: (1) {}^{3} \\ \\ \implies \: \frac{4\pi}{3}$

$So \: , total \: Number \: of \: spheres = \frac{ \frac{1000\pi}{3} }{ \frac{4\pi}{3} } \\ \\ \implies \: \cancel{\frac{1000\pi}{3} \times \frac{3}{4\pi} }\\ \\ \implies \: 250$

$\underline \mathbb{ANSWER:-}$

$\implies \: \boxed{ 250}$