V = 30 \(\times\) 25 \(\times\) 20 cm³
External box volume = 15000 cm³
Thickness of the wood = 2 cm all around
∴ Volume of the inner cuboid = 26 \(\times\) 21 \(\times\) 16 = 8736 cm³
The volume of the wooden part
Required Volume = Volume of the external box - Volume of the inner box
= 15000 - 8736
= 6264 cm³.

The volume of the cuboid formed = The volume of the cube melted.
lbh = a³

height of the cuboid = 15 cm.

V = a³ = 125000 litres
= 125 m³
a = \(\sqrt [ 3 ]{ 125{ m }^{ 3 } } =\sqrt [ 3 ]{ 5\times 5\times 5 }\)
∴ length of its side = 5 m.

(i) side of a cube (a) = 5 cm
Volume of a cube V = a³ = 5 \(\times\) 5 \(\times\) 5 = 125 cm³
a = 3.5 m
V = a³ = 3.5 \(\times\) 3.5 \(\times\) 3.5 m³ = 42.875 m³
a = 21 cm
V = a³ = 21 \(\times\) 21 \(\times\) 21 cm³ = 9261 cm³.

I = 24 cm b = 12 cm h = 8 cm
Volume of the brick = I x b x h = (24 \(\times\) 12 \(\times\) 8) cm³= 2304 cm³
Wall dimensions are:
L = 20 m = 2000 cm
B = 48 cm
H = 6 m = 600 cm
No. of brieks required to build the wall = \(\frac { Volume\ of\ the\ wall }{ Volume\ of\ a\ bricks } \)

No. of brieks required = 25000

Let 1 ratio = x then 5:4:3
⇒  5x: 4x: 3x
5x \(\times\) 4x \(\times\) 3x = 60x³ = 7500 cm³

x = 5 cm
∴ 5x = 5 \(\times\) 5 = 25 cm
4x = 4 \(\times\) 5 = 20 cm
3x = 3 \(\times\) 5 = 15 cm
∴ Dimensions of a chocolate box are 25 cm \(\times\) 20 cm \(\times\) 15 cm.

Dimensions of a match box = 6 cm \(\times\) 3.5 cm \(\times\) 2.5 cm
V = (6 \(\times\) 3.5 \(\times\) 2.5) cm³ = 52.5 cm³
Volume of 12 such boxes = 12 \(\times\) 52.5 cm³ = 630 cm³.

(i) l = 12 cm
b = 8 cm
h= 6 cm
Volume of the cuboid = lbh
= 12 \(\times\) 8 \(\times\) 6 cm³ = 576 cm³
(ii) l = 60 m 
b = 25 m 
h = 1.5 m
Volume of the cuboid = l b h = 60 \(\times\) 25\(\times\)1.5 m³ = 2250 m³

6a² = 2400 cm²
⇒ a²=\(\frac { 2400 }{ 6 } \)
∴ 4a² = \(\frac { 4\times 2400 }{ 6 } \) 
= 1600 cm².

(i) side ofa cube = 8 m
TSA of the cube = 6a² = 6 \(\times\) 64 = 384 m²
LSA of the cube = 4a² = 4 \(\times\) 64 = 256 m²
(ii) side a = 21 cm
TSA= 6a² = 6 \(\times\) 21 \(\times\) 21 = 2646 cm².
LSA = 4a² = 4 \(\times\) 21 \(\times\) 21 = 1764 cm².
(iii) side a = 7.5 cm
TSA = 6a² = 6 \(\times\) 7.5 \(\times\) 7.5 cm² = 337.5 cm²
LSA = 4a² = 4 \(\times\) 7.5 \(\times\) 7.5 cm² = 225 cm².