RD Chapter 18- Surface Areas and Volume of a Cuboid and Cube Ex-18.1 |
RD Chapter 18- Surface Areas and Volume of a Cuboid and Cube Ex-18.2 |

**Answer
1** :

Side of a cube = 6 cm

∴ Byjoining two such cubes, the length of so

formed cuboid (l) = 6 x 2 = 12 cm

Breadth (b) = 6 cm

Height (h) = 6 cm

∴ Volume= lbh = 12 x 6 x 6 cm^{3}

= 432 cm^{3}

**Answer
2** :
Ratio in the sides of three cubes = 3 : 4 : 5

Let side of first cube = 3x

and side of second cube = 4x

and side of third cube = 5x

∴ Sum of volume of threecubes

= (3x)^{3} + (4x)^{3} + (5x)^{3}

= 27x^{3} + 64x^{3} + 125x^{3} = 216x^{3}

∴ Volume of the cube formedJby melting these three cubes = 216x^{3}

Side of first cube = 3x = 3 x 2 = 6 cm

Side of second cube = 4x = 4×2 = 8 cm

and side of third cube = 5.r = 5 x 2 = 10 cm

Side of second cube = 4x = 4×2 = 8 cm

and side of third cube = 5.r = 5 x 2 = 10 cm

**Answer
3** :

Perimeterof each face of a cube = 32 cm

∴ Lengthof edge = 32/4 =8 cm

and lateral surface area of the cube = 4 x (side)^{2}

= 4 x 8 x 8 = 256 cm^{2}

**Answer
4** :

**Answer
5** :

Totalsurface area of a cuboid = 372 cm^{2}

and lateral surface area = 180 cm^{2}

∴ Areaof base and roof = 372 – 180 = 192 cm^{2}

and area of base = 192/2 =96 cm^{2}

**Answer
6** :

By joining three cubes of side 4 cm each, end is end, we get acuboid

Length of cuboid = 4 x 3 = 12 cm

Breadth = 4 cm

and height = 4 cm

∴Surface area = 2(lb + bh + hl)

= 2[12 x4+4×4 + 4x 12] cm^{2}

= 2[48 + 16 + 48] cm^{2}

= 2 x 112 = 224 cm^{2}

**Answer
7** :

Surfacearea of a cuboid = 1300 cm^{2}

Breadth (b) = 10 cm

and height (h) = 20 cm

Let l be the length, then

= 2 (lb + bh + hl) = 1300

lb+ bh + hl = 1300/2 =650

l x 10 + 10 x 20 + 20 x l = 650

10l + 20l + 200 = 650

⇒ 30l =650 – 200 = 450

⇒ l= 450/30 =15

∴ Lengthof cuboid = 15 cm

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