Question

the surface area of metallic sphere is 2464 cm² it is melted and recasted into solid right circular cones of radius 3.5 cm and height 7 cm calculate i the radius of sphere ii the number of cones recast​

Answer 1

GIVEN :

• SURFACE AREA OF METALLIC SPHERE = 2464 cm²
• RADIUS AND HEIGHT OF RIGHT CIRCULAR CONES = 3.5 cm AND 7 cm

TO FIND :

1. RADIUS OF SPHERE
2. NUMBER OF CONES RECASTED

SOLUTION :

1] SURFACE AREA OF METALLIC SPHERE = 2464 cm²

$= > 4\pi {r}^{2} = 2464 \\ \\ = > \pi {r}^{2} = 616 \\ \\ = > {r}^{2} = 616 \times \frac{7}{22} \\ \\ = > {r}^{2} = 196 \\ \\ = > r = 14cm$

2] LET THE NUMBER OF RIGHT CIRCULAR CONES BE 'n'

VOLUME OF SPHERE = VOLUME OF NUMBER OF RIGHT CIRCULAR CONES FORMED

$= > \frac{4}{3} \times \: \pi {r}^{3} = n \times \frac{\pi {r}^{2}h }{3} \\ \\ = > 4 {r}^{3} = n {r}^{2} h \\ \\ = > 4(2744) = n \times (12.25)(7) \\ \\ = > n = \frac{4(2744)}{12.25(7)} = 128$

∴ NUMBER OF RIGHT CIRCULAR CONES FORMED IS 128 AND RADIUS OF METALLIC SPHERE IS 14 cm

HOPE IT HELPS !!!!