## RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube VSAQS

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube VSAQS

Other Exercises

- RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.1
- RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2
- RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube VSAQS
- RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS

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 \(\sqrt { 3 } \) 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 = \(\frac { 32 }{ 4 }\) = 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 = \(\frac { 192 }{ 2 }\) = 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 = \(\frac { 1300 }{ 2 }\) = 650

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

10l + 20l + 200 = 650

⇒ 30l = 650 – 200 = 450

⇒ l = \(\frac { 450 }{ 30 }\) = 15

∴ Length of cuboid = 15 cm

Hope given RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube VSAQS are helpful to complete your math homework.

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