Question

Two solid spheres have surface areas of 144 pi cm square and 256 pi cm square respectively. The are melted and recast to form a larger sphere. Find the surface area of the larger sphere in square centimetres.

Answer 1

Answer:

Two solid spheres have surface areas 144 pi sq.cm and 256 pi sq.cm, respectively. They are melted and recast to form a larger sphere. Find the surface area of this sphere in sq.cm.

---------------------

Find the radii, then the volumes.

Add the volumes, find the radius of the total.

Find the surface area of the total.

$area = \: 4.\pi \: r^2$

for 144pi sq cm, r = 6

for 256pi sq cm, r = 8

$vol = \frac{4.\pi.r}{3}$

for r = 6, V = 288pi cc

for r = 8, V = 2048pi/3 cc

Total volume = 2912pi/3 cc

r =~ 8.996 cm

SA total =~ 1016.945 sq cm

=~ 323.7pi sq cm, less the the sum of the 2 original areas