a solid sphere of radius 10.5 cm is melted and than recast into smaller cones of radius 3.5 cm and height 3cm find the number of cones so formed .
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a solid sphere of radius 10.5 cm is melted and than recast into smaller cones of radius 3.5 cm and height 3cm find the number of cones so formed .
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Given : A Solid Sphere of radius 10.5 cm is melted and recast into smaller comes of radius 3.5 cm and height 3 cm
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To Find : Find the No. of Cones formed
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SolutioN :
[tex] \dag \; {\underline{\underline{\sf{ \; Let \; the \; Values \; :- }}}} [/tex]
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[tex] \dag \; {\underline{\underline{\sf{ \; Calculating \; the \; No. \; of \; Cones \; :- }}}} [/tex]
[tex] \; \; \green\dashrightarrow \; \; \red{\sf{ No. \; of \; Cones = \dfrac{ Volume \; of \; Sphere }{ Volume \; of \; Cone } }} \\ \\ \\ [/tex]
[tex] \; \; \dashrightarrow \; \; \sf{ No. \; of \; Cones = \left \lgroup \dfrac{ \bigg[ \dfrac{4}{3} \pi r^3 \bigg] }{ \bigg[ \dfrac{1}{3} \pi r^2 h \bigg] } \right \rgroup } \\ \\ \\ [/tex]
[tex] \; \; \dashrightarrow \; \; \sf{ No. \; of \; Cones = \left \lgroup \dfrac{ \bigg[ \dfrac{4}{3} \times \pi \times \bigg( r \bigg)^3 \bigg] }{ \bigg[ \dfrac{1}{3} \times \pi \times \bigg( r \bigg)^2 \times h \bigg] } \right \rgroup } \\ \\ \\ [/tex]
[tex] \; \; \dashrightarrow \; \; \sf{ No. \; of \; Cones = \left \lgroup \dfrac{ \bigg[ \dfrac{4}{3} \times \pi \times \bigg( 10.5 \bigg)^3 \bigg] }{ \bigg[ \dfrac{1}{3} \times \pi \times \bigg( 3.5 \bigg)^2 \times 3 \bigg] } \right \rgroup } \\ \\ \\ [/tex]
[tex] \; \; \dashrightarrow \; \; \sf{ No. \; of \; Cones = \left \lgroup \dfrac{ \bigg[ \dfrac{4}{3} \times \cancel{\pi} \times \bigg( 10.5 \bigg)^3 \bigg] }{ \bigg[ \dfrac{1}{3} \times \cancel{\pi} \times \bigg( 3.5 \bigg)^2 \times 3 \bigg] } \right \rgroup } \\ \\ \\ [/tex]
[tex] \; \; \dashrightarrow \; \; \sf{ No. \; of \; Cones = \left \lgroup \dfrac{ \bigg[ \dfrac{4}{3} \times 1157.625 \bigg] }{ \bigg[ \dfrac{1}{3} \times 12.25 \times 3 \bigg] } \right \rgroup } \\ \\ \\ [/tex]
[tex] \; \; \dashrightarrow \; \; \sf{ No. \; of \; Cones = \left \lgroup \dfrac{ \bigg[ \dfrac{4}{3} \times 1157.625 \bigg] }{ \bigg[ \dfrac{1}{\cancel3} \times 12.25 \times \cancel3 \bigg] } \right \rgroup } \\ \\ \\ [/tex]
[tex] \; \; \dashrightarrow \; \; \sf{ No. \; of \; Cones = \left \lgroup \dfrac{ \bigg[ \dfrac{4}{3} \times 1157.625 \bigg] }{ \bigg[ 1 \times 12.25 \bigg] } \right \rgroup } \\ \\ \\ [/tex]
[tex] \; \; \dashrightarrow \; \; \sf{ No. \; of \; Cones = \left \lgroup \dfrac{ \bigg[ \dfrac{4}{\cancel3} \times \cancel{1157.625} \bigg] }{ \bigg[ 1 \times 12.25 \bigg] } \right \rgroup } \\ \\ \\ [/tex]
[tex] \; \; \dashrightarrow \; \; \sf{ No. \; of \; Cones = \left \lgroup \dfrac{ \bigg[ 4 \times 385.875 \bigg] }{ \bigg[ 1 \times 12.25 \bigg] } \right \rgroup } \\ \\ \\ [/tex]
[tex] \; \; \dashrightarrow \; \; \sf{ No. \; of \; Cones = \left \lgroup \dfrac{ \bigg[ 4 \times 385.875 \bigg] }{ \bigg[ 12.25 \bigg] } \right \rgroup } \\ \\ \\ [/tex]
[tex] \; \; \dashrightarrow \; \; \sf{ No. \; of \; Cones = \left \lgroup \dfrac{1543.5}{12.25} \right \rgroup } \\ \\ \\ [/tex]
[tex] \; \; \dashrightarrow \; \; \sf{ No. \; of \; Cones = \left \lgroup \; \cancel\dfrac{1543.5}{12.25} \; \right \rgroup } \\ \\ \\ [/tex]
[tex] \; \; \dashrightarrow \; \; {\pmb{\underline{\boxed{\orange{\frak{ No. \; of \; Cones = 126 }}}}}} \; \bigstar \\ \\ \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \qquad \; \therefore \; [/tex] Number of Cones formed by melting the Sphere is 126
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126 cones
126 conesA metallic sphere of radius 10.5cm is melted and then recast into smaller cones, each of radius 3.5cm and height 3cm. How many cones are obtained? Therefore, 126 cones are obtained from the metallic sphere.