Question
Some solid metallic right circular cones, each with radius of the base 3 cm and height 4 cm, are melted to form a solid sphere of radius 6 cm. The number of right circular cones is :
Answer: Option C
Volume of sphere :
$$\eqalign{
& = \left( {\frac{4}{3}\pi \times {6^3}} \right){\text{c}}{{\text{m}}^{\text{3}}} \cr
& = \left( {288\pi } \right){\text{c}}{{\text{m}}^{\text{3}}} \cr} $$
Volume of each cone :
$$\eqalign{
& = \left( {\frac{1}{3}\pi \times {3^2} \times 4} \right){\text{c}}{{\text{m}}^{\text{3}}} \cr
& = \left( {12\pi } \right){\text{c}}{{\text{m}}^{\text{3}}} \cr} $$
∴ Number of cone :
$$\eqalign{
& = \frac{{288\pi }}{{12\pi }} \cr
& = 24 \cr} $$
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Volume of sphere :
$$\eqalign{
& = \left( {\frac{4}{3}\pi \times {6^3}} \right){\text{c}}{{\text{m}}^{\text{3}}} \cr
& = \left( {288\pi } \right){\text{c}}{{\text{m}}^{\text{3}}} \cr} $$
Volume of each cone :
$$\eqalign{
& = \left( {\frac{1}{3}\pi \times {3^2} \times 4} \right){\text{c}}{{\text{m}}^{\text{3}}} \cr
& = \left( {12\pi } \right){\text{c}}{{\text{m}}^{\text{3}}} \cr} $$
∴ Number of cone :
$$\eqalign{
& = \frac{{288\pi }}{{12\pi }} \cr
& = 24 \cr} $$
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