15 identical solid metallic spheres of radius 3 cm are melted to form a single solid sphere. 259.97 cm³ of the material was lost in the process. What is the surface area of the newly formed sphere? |
435.96 cm² 159.63 cm² 554 cm² 616 cm² |
616 cm² |
Volume of 15 smaller spheres = 15 \(\frac{4}{3}\) \(\pi \) (3)³ = 1695.6 cm³ Given, 259.97 cm³ was lost Thus Volume of new sphere = 1435.63cm³ = \(\frac{4}{3}\) \(\pi \) (r)³ r = 7 cm Surface area = 4 \(\pi \) r² = 616 cm² |