Cube
Side (a) = 12cm
Cuboid
length (l) = 18cm
breadth (b) = 16cm
height (h) = ?
Here, Volume of the Cuboid =Volume of the Cube
l × b × h = a³
18 ×16 × h = 12 ×12 ×12
h = \(\frac{12\times12\times12}{18\times16}\)
h = 6 cm
Therefore, the height of the cuboid is 6 cm

Let ‘a’ be the side of cubical tank.
Here, volume of the tank = 64,000 litres
i.e., a³ = 64,000 = \(\frac{64000}{1000}\) [since,1000 litres = 1m³ ]
a³ = 64 m³
a =\(\sqrt [ 3 ]{ 64 } \) a = 4 m
Therefore, length of the side of the tank is 4 metres.

Let ‘a’ be the side of the cube.
Given that, total surface area = 864 cm²
6a²= 864
a² = \(\frac{864}{6}\)
a² = 144
Therefore, side (a) = 12 cm
Now, volume of the cube = a³
= 123 = 12 ×12 ×12 = 1728 cm³

Given that side (a) = 10 cm
volume of the cube = a³
= 10 × 10 × 10
= 1000 cm³

Here, the dimensions of a sweet box are Length (l) = 22cm, breadth (b) = 18cm,
height (h) = 10 cm.
Volume of a sweet box = l × b × h
= 22 × 18 × 10 cm³
The dimensions of a carton are
Length (l) = 1m= 100 cm, breadth (b) = 88 cm,
height (h) = 63 cm.

Volume of the carton = l × b × h
= 100 × 88 × 63 cm³
The number of sweet boxes packed =\(\frac{volume \ of \ the \ carton}{volume\ of \ a \ sweet \ box}\)
= \(\frac{100 \times 88\times63}{22\times18\times10}\)
= 140 boxes

Length of the fish tank l =3.8 m
Breadth of the fish tank b =2.5 m ,
Height of the fish tank h =1.6 m
Volume of the fish tank = l × b × h
= 3.8 × 2.5 ×1.6
= 15.2 m³
= 15.2 ×1000 litres
= 15200 litres

Let the dimensions of the cuboid be
l = 7x, b = 5x and h = 2x.
Given that volume of cuboid = 35840 cm³
l × b × h = 35840
(7x)(5x)(2x) = 35840
70x³ = 35840
x³ = \(\frac{35840}{70}\)
x² = 512
x =\(\sqrt [ 3 ]{ 8\times 8\times 8 } \)
x = 8 cm
Length of cuboid= 7x = 7 × 8 = 56cm
Breadth of cuboid= 5x = 5 × 8 = 40cm
Height of cuboid= 2x = 2 × 8 = 16 cm

Since both breadth and height are given in cm, it is necessary to convert the length also in cm.
So we get, l = 120 mm = \(\frac{120}{10}\) = 12cm and take b = 10 cm, h = 8 cm as such.
Volume of a cuboid = l × b × h

= 12 ×10 × 8
= 960 cm³
Volume of 10 such cuboids= 10 × 960
= 9600 cm³

The side of the cube (a) = 5 cm
Total Surface Area = 6a² = 6(5²) = 150 sq. cm
Lateral Surface Area = 4a² = 4(5²) = 100 sq. cm

Here, length (l) = 25 m, breadth (b) =15 m, height (h) = 5 m.
Area of four walls = LSA of cuboid
= 2(l + b) × h
= 2(25 +15) × 5
= 80 × 5 = 400 m²
Area of the floor = l × b

= 25 ×15
= 375 m²
Total renovating area of the hall = (Area of four walls + Area of the floor) = (400 + 375) m² = 775 m²
Therefore, cost of renovating at the rate of Rs.80 per m² = 80 × 775
= Rs. 62,000