Case Study
Manish is a carpenter. One day, he made an open cubical box of internal edge 18 cm. The thickness of the plywood is 1 cm. He painted the inner surface of the box black and the outer lateral surfaces as green.

Based on the above information, answer the following questions:

1. Total area to be painted black is :
   (a) 1600 cm²
   (b) 1620 cm²
   (c) 1650 cm²
   (d) 1680 cm²

2. Length of the outer edge of the box is :
   (a) 20 cm
   (b) 19 cm
   (c) 18 cm
   (d) 18.5 cm

3. Total outer lateral surface area to be painted green is :
   (a) 1500 cm²
   (b) 1510 cm²
   (c) 1520 cm²
   (d) 1600 cm²

4. Total outer surface area of the box (excluding the top) is :
   (a) 1900 cm²
   (b) 1920 cm²
   (c) 2000 cm²
   (d) 2320 cm²

5. Length of the longest rod that can fit inside the box is :
   (a) 18 cm
   (b) 19 cm
   (c) 20 cm
   (d) 3 cm

Assertion (A) : The length of the longest rod that can be put in a room of dimensions 10 m × 10 m × 5 m is 15 m.

Reason (R) : Length of the diagonal of a cuboid = $\sqrt{l^2 + b^2 + h^2}$

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

The area of a base of a cuboidal water tank is 6500 cm² and the volume of water contained in it is 2.6 m³. The depth of the water is :

1. 5 m

2. 4 m

3. 3.5 m

4. 3 m

The volume of a cuboid of dimensions x, y and z is V and its surface area is S. The value of $\dfrac{1}{V}$ is :

1. $\dfrac{2}{S}\Big(\dfrac{1}{x} + \dfrac{1}{y} + \dfrac{1}{z}\Big)$

2. $\dfrac{S}{2} \Big(\dfrac{1}{x} + \dfrac{1}{y} + \dfrac{1}{z}\Big)$

3. $\dfrac{3}{S} \Big(\dfrac{1}{x} - \dfrac{1}{y} - \dfrac{1}{z}\Big)$

4. $\dfrac{S}{3} \Big(\dfrac{a + b + c}{abc}\Big)$