## Mensuration

Very Short Q and A

Q1: Find the volume of cube whose edge is 3x?

Q2: The volume of a cuboid of dimensions 5a × 3b × 2c is?

Q3: The maximum length of a rod that can be kept in cuboidal box 12 cm × 9 cm × 8cm?

Q4: The lateral surface area of a cuboid of dimension 11 cm × 8 cm × 5 cm is:

Q5: The sum of the areas of all six faces of a cuboid is the ________ of the Cuboid.

Q6: The volume of a cube is 2,197 cm³. Find its surface area.

Q7: The volume of an oil tank is 4m³. Its capacity in litres is _______.

Q8: The cost of painting the total surface area of a cube at the rate of 20 paise per cm² is ₹888.80.
Find the volume of the cube.

Q9: Find the surface area of of an 'open box' whose length, breadth and height are l, b and h respectively.

Q10: The edges of a cuboid are in the ratio 1 : 2 : 3 and its surface area is 88 cm². Find the volume of the cuboid?

Volume of cube = a³ Here a = 3x. ∴ V = (3x)³ = 27x³

V = length × breadth × height
V = 5a × 3b × 2c = 30abc

l = 12cm, b = 9cm, h = 8cm

```diagonal d = √(l² + b² + h²)
________________
= √(12² + 9² + 8²)
________________
= √(144 + 81 + 64)
____
= √289  = 17cm

```

LSA = 2h(l + b) = 2()
= 2×5×(11 + 8)
= 10 × 19
= 190 cm²

Vol of cube = a³ = 2197 = 13³
⇒ a = 13cm
TSA = 4a² = 4 × 13 × 13 = 676 cm²

Note 1m³ = 1000 litres

TSA = 388.80/0.2 = 1944 cm²
TSA = 6a² = 1944 cm²
∴ a² = 324
⇒ a = √(324) = 18cm
V = a³ = 18³ = 5832 cm³

Answer 9: 2bh + 2hl + lb

Let l = x, b = 2x and h = 3x
TSA = 2(lb + bh + hl) = 88
2x² + 6x² + 3x² = 44
11x² = 44
x = 2
∴ l = 2cm, b = 4cm and h = 6cm
Volume = l × b × h
= 2 × 4 × 6 = 48 cm³