## 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?

Answer 1: 27x³

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

Answer 2: 20abc

V = length × breadth × height

V = 5a × 3b × 2c = 30abc

Answer 3: 17cm

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

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

Answer 4: 190cm²

LSA = 2h(l + b) = 2()

= 2×5×(11 + 8)

= 10 × 19

= 190 cm²

Answer 5: surface area

Answer 6: 676 cm²

Vol of cube = a³ = 2197 = 13³

⇒ a = 13cm

TSA = 4a² = 4 × 13 × 13 = 676 cm²

Answer 7: 4000 litres

Note 1m³ = 1000 litres

Answer 8: 5832 cm³

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

Answer 10:

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

## No comments:

## Post a Comment

We love to hear your thoughts about this post!