When two identical cones are joined along their base, the shape so formed will be as shown in figure

So,

Total surface area of shape formed = Curved area of first cone + Curved surface area of second cone

= 2(Surface area of cone)

[since, both cones are identical]

Now, As we know,

Surface area of cone = πrl,

where r = radius and l = slant height

Total Surface area of shape so formed = 2πrl

Given,

Radius, r = 8 cm

Height, h = 15 cm

So,

Area = 2(3.14)(8)(15) = 753.6 cm²