DAV Class 8 Maths Chapter 14 Worksheet 5 Solutions

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 cm³

Question 2.
Find the height of a cuboid whose volume is 275 cm³ and the base area is 25 cm².
Solution:
Base area lb = 25 cm²
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 cm³
Volume of 1 small cube = 6 × 6 × 6 cm³
∴ 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 = 6l² cm² and its volume = l³ cm³
Now the edge of the cube = 2l cm
∴ Its surface area = 6(2l)²
= 6 × 4l²
= 24l² cm
and its volume = (2l)³ = 8l³
(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 cm³
∴ Volume of such 12 boxes = 12 × 15 = 180 cm³

Question 6.
The volume of a cube is 1000 cm³. Find its total surface area.
Solution:
Volume of cube = l³
⇒ l³ = 1000
⇒ l = \((1000)^{1 / 3}\) = 10 cm
The total surface area of the cube = 6l²
= 6 × 10 × 10
= 600 cm²

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 cm³
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 cm³
∴ 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 cm³
Hence, the volume of the new single cube = 1728 cm³

Question 9.
Find the volume of a cube whose surface area is 150 m².
Solution:
∴ Surface area of a cube = 6l²
⇒ 6l² = 150
⇒ l² = 25
⇒ l = 5 m
∴ The volume of the cube = l³
= (5)³
= 125 m³

Question 10.
Find the volume of a cube, one face of which has an area of 81 m².
Solution:
Area of each face of a cube = l² m
⇒ l² = 81
⇒ l = 9 m
∴ The volume of the cube = l³
= (9)³
= 729 m³