The DAV Maths Book Class 8 Solutions Pdf and **DAV Class 8 Maths Chapter 14 Worksheet 5** Solutions of Mensuration offer comprehensive answers to textbook questions.

## DAV Class 8 Maths Ch 14 WS 5 Solutions

Question 1.

Two cubes each side 6 cm are joined together. Name the new solid formed and, also find its volume.

Solution:

The new solid formed is a cuboid whose length is 6 + 6 = 12 cm, breadth = 6 cm and height = 6 cm

∴ Volume of the cuboid = l × b × h

= 12 × 6 × 6

= 432 cm^{3}

Question 2.

Find the height of a cuboid whose volume is 275 cm^{3} and the base area is 25 cm^{2}.

Solution:

Base area lb = 25 cm^{2}

Volume of the cuboid = l × b × h

⇒ 275 = 25 × h

⇒ h = \(\frac{275}{25}\) = 11 cm

Hence, the required height = 11 cm

Question 3.

The dimensions of a box are 60 cm × 54 cm × 30 cm. How many small cubes of side 6 cm can be placed in the box?

Solution:

Volume of the box = 60 × 54 × 30 cm^{3}

Volume of 1 small cube = 6 × 6 × 6 cm^{3}

∴ Number of cubes that can be placed in the box = \(\frac{Volume of the box}{Volume of the small cube}\)

= \(\frac{60 \times 54 \times 30}{6 \times 6 \times 6}\)

= 450

Hence, the required number of cubes = 450

Question 4.

If each edge of a cube is doubled,

(i) How many times will its surface area increase?

(ii) How many times will its volume increase?

Solution:

Let the edge of a cube be l cm.

∴ Its surface area = 6l^{2} cm^{2} and its volume = l^{3} cm^{3}

Now the edge of the cube = 2l cm

∴ Its surface area = 6(2l)^{2}

= 6 × 4l^{2}

= 24l^{2} cm

and its volume = (2l)^{3} = 8l^{3}

(I) New surface area increased by original surface area = \(\frac{24 l^2}{6 l^2}\) = 4 times

(ii) New volume increased by original volume = \(\frac{8 l^3}{l^3}\) = 8 times.

Hence, (i) the surface area will increase 4 times and (ii) the volume will increase 8 times.

Question 5.

A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What will be the volume of a packet containing 12 such boxes?

Solution:

Volume of one box = 4 × 2.5 × 1.5 cm = 15 cm^{3}

∴ Volume of such 12 boxes = 12 × 15 = 180 cm^{3}

Question 6.

The volume of a cube is 1000 cm^{3}. Find its total surface area.

Solution:

Volume of cube = l^{3}

⇒ l^{3} = 1000

⇒ l = \((1000)^{1 / 3}\) = 10 cm

The total surface area of the cube = 6l^{2}

= 6 × 10 × 10

= 600 cm^{2}

Question 7.

How many planks each of which is 2 m long, 2.5 cm broad, and 4 cm thick can be cut off from a wooden block 6 m long, 15 cm broad, and 40 cm thick?

Solution:

Length of the plank = 2 m

= 2 × 100

= 200 cm

breadth = 2.5 cm and height = 4 cm

∴ Its volume = l × b × h

= 200 × 2.5 × 4

= 2000 cm^{3}

Now the length of the wooden block = 6 m

= 6 × 100

= 600 cm

breadth = 15 cm and height = 40 cm

∴ Its volume = 600 × 15 × 40 = 360000 cm^{3}

∴ Number of planks = \(\frac{Volume of the block}{Volume of plank }\)

= \(\frac{360000}{2000}\)

= 180

Hence, the required number of planks = 180.

Question 8.

Three solid metal cubes with edges 6 cm, 8 cm, and 10 cm respectively are melted together and formed into a single cube. Find the volume of the new cube.

Solution:

Combined volume of the 3 cubes = (6)^{3} + (8)^{3} + (10)^{3}

= 216 + 512 + 1000

= 1728 cm^{3}

Hence, the volume of the new single cube = 1728 cm^{3}

Question 9.

Find the volume of a cube whose surface area is 150 m^{2}.

Solution:

∴ Surface area of a cube = 6l^{2}

⇒ 6l^{2} = 150

⇒ l^{2} = 25

⇒ l = 5 m

∴ The volume of the cube = l^{3}

= (5)^{3}

= 125 m^{3}

Question 10.

Find the volume of a cube, one face of which has an area of 81 m^{2}.

Solution:

Area of each face of a cube = l^{2} m

⇒ l^{2} = 81

⇒ l = 9 m

∴ The volume of the cube = l^{3}

= (9)^{3}

= 729 m^{3}