2 cubes each of volume 64 cm³ are joined end to end. Find the surface area of the resulting cuboid.

Let ‘a’ be the length of a side of a cube. Then
Volume of one cube = 64 cm³
⇒    n³ = 65 cm³
⇒    n = 4 cm
On joining the cubes, a cuboid is formed.
Then The length of the resulting cuboid (l) = 2
The breadth of the resulting cuboid (b) = a cm
The thickness of the resulting cuboid (h) = a cm
Now,
Surface area of the resulting cuboid
= 2(lb + bh + hl)
= 2 (2a. a + a. a + a. 2a)
= 2 (2a² + a² + 2a²)
= 2 (5a²) = 10a² = 10 (4)²
= 160 cm².

Let r cm be the radius of the cylinder and h cm be the height of the cylinder, then
r = 7 cm,
and    h = (13–7) cm
= 6 cm.
Let r₁ cm be the radius of the hemisphere, then
r₁ = 7 cm
Now,
the inner curved surface area of the vessel
= C,S.A of hemisphere
+ C,S.A of cylinder
= (2πr₁² + 2 π rh) cm²
= (2 π r² + 2 π rh) cm² [∵ r₁ = r]
= [2 π r (r + h)] cm²

= (44 x 13) cm²
= 572 cm².

r = 3.5 cm,
h = (15.5 – 3.5) cm = 12 cm.
Now,   l = 

 Let r₁ cm be the radius of the hemisphere.
Then, r₁ = 3.5 cm    [∵ r = r₁]
Now,
The total surface area of the toy
= CSA of hemisphere
+ CSA of cone
= 2 π r₁² + πrl
= 2π r² + πrl    [ ∵ r₁= r]
= π r [2r + l]

Let a be the length of an edge of the cube. Then
a = 7 cm
Greatest diameter of the hemisphere
= Length of an edge of the cube
= 7 cm
Now,
Surface area of the cube
= 6 (edge)²
= 6 x 7²
= 6 x 49 = 294 cm²
Let r be the radius of the hemisphere.
Then,       r = 
Now,  
Curbed surface area of hemisphere

And,  Base area = 
                              
Total surface area
= Surface area of the cube + curved surface area of the hemisphere – base area of the hemisphere