In this chapter, we provide RD Sharma Solutions for Chapter 18 Surface Areas and Volume of a Cuboid and Cube VSAQS for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Solutions for Chapter 18 Surface Areas and Volume of a Cuboid and Cube VSAQS Maths pdf, free RD Sharma Solutions for Chapter 18 Surface Areas and Volume of a Cuboid and Cube VSAQS Maths book pdf download. Now you will get step by step solution to each question.

Textbook | NCERT |

Class | Class 9 |

Subject | Maths |

Chapter | Chapter 18 |

Chapter Name | Surface Areas and Volume of a Cuboid and Cube |

Exercise | VSAQS |

**RD Sharma Solutions for Class 9 Chapter 18 Surface Areas and Volume of a Cuboid and Cube VSAQS Download PDF**

Question 1.

If two cubes of side 6 cm are joined face to face, then find the volume of the resulting cuboid.

Solution:

Side of a cube = 6 cm

∴ By joining 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}

Question 2.

Three cubes of metal whose edges are in the ratio 3 : 4 : 5, are melted down into a single cube whose diagonals is 12 3–√ cm. Find the edges of three cubes.

Solution:

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 three cubes

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

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

∴ Volume of the cube formed Jby 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

Question 3.

If the perimeter of each face of a cube is 32 cm, find its lateral surface area. Note that four faces which meet the base of a cube are called its lateral faces.

Solution:

Perimeter of each face of a cube = 32 cm

∴ Length of edge = 324 = 8 cm

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

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

Question 4.

Find the edge of a cube whose surface area is 432 m^{2}.

Solution:

Question 5.

A cuboid has total surface area of 372 cm^{2} and its lateral surface area is 180 cm^{2}, find the area of its base.

Solution:

Total surface area of a cuboid = 372 cm^{2}

and lateral surface area = 180 cm^{2}

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

and area of base = 1922 = 96 cm^{2}

Question 6.

Three cubes of each side 4 cm are joined end to end. Find the surface area of the resulting cuboid.

Solution:

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

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}

Question 7.

The surface area of a cuboid is 1300 cm2. If its breadth is 10 cm and height is 20 cm, find its length.

Solution:

Surface area 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 = 13002 = 650

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

10l + 20l + 200 = 650

⇒ 30l = 650 – 200 = 450

⇒ l = 45030 = 15

∴ Length of cuboid = 15 cm

**All Chapter RD Sharma Solutions For Class 9 Maths**

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**All Subject NCERT Solutions For Class 9**

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