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##### Question 1. There are two cuboidal boxes as shown in the given figure. Which box requires the less amount of material to make?

Solution:
Volume of a cuboid V1= lbh
= 60 × 40 × 50
V1= 1,20,000 cubic units.
Volume of a cube V2= (a)3
= (50)3= 50 × 50 × 50
V2= 1,25,000 cubic units.
∴ The cuboidal box requires less amount of material.
∴ V1< V2

##### Question 2. Find the side of a cube whose surface area is 600 cm2

Solution:
Total surface area of a cube = 6a2
⇒ 6a2= 600
⇒ a2=[latex]600/6[/latex] = 100
⇒ a2= 100
⇒ a = √100 = 10
∴ The side of a cube (a) = 10 cm.

##### Question 3. Prameela painted the outer surface of a cabinet of measures 1m × 2m × 1 .5m. Find the surface area she cover if she painted all except the bottom of the cabinet?

Solution:
The area of outer surface of a cabinet except the bottom of the cabinet will be equal to its lateral surface area.
I = lm,b = 2m, h = 1.5m.
A = 2h(l + b)
= 2 × 1.5(1 + 2)
= 3 × 3 = 9 m2.

##### Question 4. Find the cost of painting a cuboid of dimensions 20cm × 15 cm × 12 cm at the rate of 5 paisa per square centimeter.

Solution:
l = 20cm, b = 15cm, h = 12cm.
∴ Total surface area of a cuboid
A = 2 (lb + bh + lh)
=2(20 × 15 + 15 × 12 + 20 × 12)
= 2 (300 + 180 + 240)
= 2 × 720
= 1440 sq.cm.
The cost of painting a cuboid at the rate of 5 paisa per sq. cm for 1440 sq.cm.
= 1440 × 5 paisa
= 7200 paise
= ₹7200/100
= ₹ 72

Solution

Solution

##### Question 3. What will happen to the volume of a cube if the length of its edge is reduced to half? Is the volume get reduced? If yes, how much?

Solution:
Volume of a cube of side (s) is V1= a3
If the length of the side is reduced by half then
s =a/2
∴ Volume of cube (V2) = s3

∴ V2=1/8 × V1
∴ V1= 8V2

##### Question 4. Find the volume of each of the cube whose sides are.

(i) 6.4 cm
(ii) 1.3 m
(iii) 1.6 m.
Solution:
Volume of a cube(V) = a3

i) a = 6.4 cm
ii) a = 1.3 m
iii) a = 1.6 m

V = (6.4)3
Volume of a cube (V) = a3
= 6.4 × 6.4 × 6.4
= 262.144 cm3

V = (1.3)3
= 1.3 × 1.3 × 1.3
= 2.197 m3

V = (1.6)3
= 1.6 × 1.6 × 1.6
= 4.096 m3

##### Question 5. How many bricks will be required to build a wall of 8 m long, 6m height and 22.5 cm thici if each brick measures 25 cm by 11.25 cm by 6 cm?

Solution:
The volume of a wall of measures
8 m × 22.5 cm × 6 m
(V1) = l1b1h1
= 8 m × 22.5 cm × 6 m
= 800 cm × 22.5 cm × 600 cm
The volume of a brick each measures
25 cm × 11.25 cm × 6 cm
(V2) = l2b2h2
= 25 × 11.25 × 6 cm3
∴ The no.of bricks will be required

= 32 × 2 × 100 = 6400

##### Question 6. A cuboid is 25 cm long, 15 cm broad, and 8 cm high . How much of its volume will differ from that of a cube with the edge of 16 cm’?

Solution:
Volume of a cuboid (V1) of measures
= 25 cm, b = 15 cm, h = 8 cm.
V1= 25 × 15 × 8 = 3000 cm3
Volume of a cube of measure side (s) = 16 cm is
V2= (s)3= (16)3= 16 × 16 × 16
= 4096 cm3
The difference between their volumes
= V2- V1
= 4096 - 3000
= 1096 cm3

##### Question 7. A closed box is made up of wood which is 1cm thick .The outer dimensions of the box is 5 cm × 4 cm × 7 cm. Find the volume of the wood used.

Solution:
The volume of a box formed with outer measures 5 cm × 4 cm × 7 cm
V1= l × b × h
= 5 × 4 × 7
∴ V1= 140 cm3
Inner measures
= l - 2w, b - 2w, h - 2w
= (5 - 2 × 1), (4 - 2 × 1), (7 - 2 × 1)
= (5 - 2), (4 - 2), (7 - 2)
= 3 cm, 2 cm, 5 cm
∴ Volume of a box formed with inner measures
V2= (l - 2w)(b - 2w)(h - 2w)
= 3 × 2 × 5 = 30 cm3
∴ The volume of wood used = V1- V2
= 140 - 30 = 110 cm3

##### Question 8. How many cubes of edge 4cm, each can be cut out from cuboid whose length, breadth and height are 20 cm, 18 cm and 16 cm respectively

Solution:
The volume of a cuboid formed with the measures 20 cm × 18 cm × 16 cm
(V1) = l1b1h1= 20 × 18 × 16
Volume of a cube (V2) = s3
s = 4 cm (given)
∴ V2= (s)3= (4)3= 4 × 4 × 4 cm3
∴ No.of cubes are required
=V1/V2=20×18×16/4×4×4
= 90

##### Question 9. How many cuboids of size 4 cm × 3 cm × 2 cm can be made from a cuboid of size 12 cm x 9cm x 6cm?

Solution:
Volume of a cuboid of measures 12 cm × 9 cm × 6 cm
V1= l × b × h = 12 × 9 × 6
Volume of the smaller cuboid of measures 4 cm × 3 cm × 2 cm
V2= l2b2h2= 4 × 3 × 2
=V1/Vi = 12×9×6/4×3×2= 27

##### Question 10. A vessel in the shape of a cuboid is 30 cm long and 25 cm wide. What should be its height to hold 4.5 litres of water ?

Solution:
Length of a cuboidal vessel (l) = 30 cm
height (h) = ?
The volume of water m a cuboidal vessel = 4.5 Lts.
= 4.5 × 1000 cm3
= 4500 cm3
∴ l × b ×h = 4500
⇒ 30 × 25 × h = 4500
⇒h =4500/30×25
∴ h = 6 cm
∴ Height of the vessel (h) = 6 cm