**Surface Area
and Volume Class 9 Worksheets with Answers**

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**Surface Area
and Volume Class 9 Worksheet 1**

**1.
**An open wooden box having external dimensions
60 cm × 50 cm × 35 cm is made up of 1.5 cm thick wood. Find

a.
the capacity of the wooden box.

b.
the volume of the wood used.

**2.
**Match the dimensions of the cube and cuboid
with its correct volume, surface area or lateral surface area.

a.
Length = 6 cm, breadth = 5 cm, height = 4 cm i. 125 cm^{3}

b.
Side of a cube = 5 cm ii. 384 cm^{2}

c.
Side of a cube = 8 cm iii.
34 cm^{2}

d.
Length = 2 cm, breadth = 1.5 cm, height = 4 cm iv.
13 m^{2}

e.
Length = 3 m, breadth = 25 cm, height = 2 m v.
120 cm^{3}

**3.
**The total surface area of a cube is 2166 cm^{2}.
What is its volume?

**4.
**Find the length of the longest rod which can
be put in a room of dimension 16 m × 15 m × 12 m.

**5.
**The length, breadth and height of a cuboid are
in the ratio 4 : 3 : 2. The volume of the cuboid is 1536 m^{3}. What
are the dimensions of the cuboid?

**6.
**If the surface area of a cube is 54 cm^{3}.
Find the length of its diagonal correct to one decimal place.

**7.
**How many persons can be accommodated in an
auditorium of dimension 30 m, 26 m and 20 cm, if it is assumed that each person
requires 8 m^{3} of air?

**8.
**The surface area of a cuboid is 264 cm^{2}.
If its length and breadth are 8 cm and 6 cm respectively, calculate the height
of the cuboid.

**9.
**The volume of a water tank is 1728 m^{3}.
If it is 8 m wide and its length and height are in the ratio 2 : 3, then find
the length and height of the water tank.

**10. **The ratio of the surface area of two cubes is 49 : 144. What is
the ratio of their sides? Also, find the ratio of their volume.

**11. **The volume of a cube is 13.824 cm^{3}. Find the length of
its edge and hence find its surface area.

**12. **A hall is 12 m long and 8 m wide. If the sum
of the area of the floor and ceiling is equal to the area of its four walls,
then find the volume of the hall.

**13. **The lateral surface area of a cube is 49 cm^{2}.
Find the length of its edge and hence find its volume.

**14.
**Find the length of a diagonal of a cube whose
side measures the following (take √3 = 1.73):

a. 5.4 cm

b. 7
cm

**15.
**The dimension of a room are 12 cm × 8 cm × 6
cm. Find the cost of painting its wall at the rate of ₹ 10 per cm^{2}.

**16. **A metallic sheet is of rectangular shape with dimensions 24 cm ×
18 cm. From each of its corner, a square of side 5 cm is cut off so as to make
an open box. What is the volume of the box?

**Surface Area
and Volume Class 9 Worksheet 2**

**1.
**A solid cube is cut into two cuboids of equal
volume. Find the ratio of the total surface area of the given cube to that of
one of the cuboids.

**2. **Length of a classroom is two times its height and its breadth is 1^{1}/_{2}
times its height. The cost of whitewashing the walls at the rate of ₹ 1.60 per
m^{2} is ₹ 179.20. Find the cost of tiling the floor at the rate of ₹ 6.75 per m^{2}.

**3. **If each edge of a cube of volume V is doubled,
then find the volume of the new cube.

**4. **The outer dimensions of a closed wooden box are 10 cm × 8 cm × 7
cm. If the thickness of the wood is 1 cm, find the total cost of wood required
to make the box if 1 cm^{3} of wood costs ₹ 2.

**5. **Three cubes each of side 5 cm are joined end-to-end. Find the surface
area of the resulting cuboid.

**6.
**The capacity of a cuboidal tank is 50,000
litres. Find the breadth of the tank if its length and depth are 2.5 m and 10 m
respectively.

**7. **The dimensions of a rectangular box are in the ratio 2 : 3 : 4 and
difference between the cost of covering its four walls with a sheet of paper at
the rate of ₹ 4 per square metre and top and bottom at the rate of ₹ 4.50 per
square metre is ₹ 424. Find the dimensions of the box.

**8. **A granary is in the shape of a cuboid of size 8 m × 6 m × 3 m. If
a bag of grain occupies a space of 0.60 m^{3}, how many bags can be
stored in the granary?

**9. **A cuboid has total surface area 40 m^{2} and its lateral
surface area is 26 m^{2}. Find the area of its base.

**10.
**The total surface area of a cuboid is 7502 cm^{2}.
If its length, breadth and height are given in the ratio 2 : 3 : 5, then find
the lateral surface area of the cuboid.

**11. **A solid cube of side 12 cm is cut into 8 cubes of equal volume.
What will be the side of one new cube? Also, find the ratio between surface
areas of the new cube to the original cube.

**12. **The sum of the length, breadth and depth of a cuboid is 19 cm and
the length of its diagonal is 11 cm. Find the surface area of the cuboid.

**Surface Area
and Volume Class 9 Worksheet 3**

**1. **A solid cube of each side 24 cm is melted and recasted into solid
cuboids measuring 9 cm by 6 cm by 4 cm. Find the number of cuboids formed.

**2.
**Fill in the blanks in each of the following:

a.
The volume of air in a room of dimension 16 m by 10 m by 6 m is ___________.

b.
The volume of a cube is 343 cm^{3}, hence each side of the cube is
___________.

c.
The surface area of 4 side surfaces of a box with sides 30 cm by 50 cm by 16 cm
is equal to ___________.

d.
The volume of a cube is 1331 cm^{3}. Total surface area of the cube is
___________.

e.
In a box, 9 smaller boxes measuring 6 cm by 4.5 cm by 3 cm are completely
fitted. The volume of the bigger box ___________.

**3.
**Choose the correct option for each of the
following:

a.
Volume of a cube of side *x *cm is

i.
*x*^{2}

ii. *x*^{3
}

iii. 4*x *

iv. 4*x*^{2}

b.
Volume of a tank with a square base area 4900 cm^{2} and height 60 cm is

i.
294 cm^{2}

ii.
294000 cm^{3}

iii. 29.4
cm^{3 }

iv. 4200 cm

c.
Volume of a cube is 27000000 cm^{3}, hence its volume in m^{3} is

i.
27 m^{3 }

ii. 270 m^{3}

iii. 27000 m^{3}

iv. 30 m

d.
A closed box is of dimensions 10 cm by 8 cm by 3 cm, then its surface area is

i.
240 cm^{2}

ii. 216 cm^{2}

iii. 268 cm^{2}

iv. 80 cm^{2}

**4.
**Match the following with the correct option:

a. Volume of a cuboid is 62.5 m and if
its length is 10 m and height 1.25 m,

then breadth is i.
343 cm^{3}

b.
If surface area of a cube is 294 cm^{2}, then its volume is ii. 5 m

c.
Volume of a cube is 3375 cm^{3}, then its edge is iii. 1000000

d. 1 m^{3 }in
cm^{3} is iv.
15 cm

**5.
**Lateral surface area of a cube is 256 cm^{2}.
Find the length of its side and its volume.

**6. **Five cubes each of side 7 cm are joined end to end. Find the
volume of the resulting cuboid.

**7. **Find the number of bricks measuring 20 cm by 8 cm by 4.5 cm,
required to build a wall 9 m by 5 m by 3 m.

**8. **Find the length of a cuboid of breadth 10 cm
and height 9 cm having lateral surface area 360 cm^{2}?

**ANSWERS**

**Worksheet 1**

1. a. 89,746.5
cm^{3}

b. 15,253.5 cm^{3 }

2. a. v b. i

c. ii d. iii

e. iv

3. 6859 cm^{3
}4. 25 m

5. 16 m × 12 m × 8 m

6. 5.2 cm 7. 1950 persons

8. 6 cm 9. 12m; 18 m

10. 7 : 12; 343 : 1728

11. 2.4 cm; 34.56 cm^{2}

12. 460.8 m^{3}

13. 3.5 cm; 42.875 cm^{3}

14. a. 9.342 cm b. 12.11 cm

15. ₹ 2400 16. 560 cm^{3}

**Worksheet 2**

1. 3 : 2 2. ₹ 324

3. 8V 4. ₹ 640

5. 350 cm^{3} 6. 2 m

7. 4 m × 6 m × 8 m

8. 240 bags 9. 7 m^{2}

10. 6050 cm^{2}

11. 6 cm; 1 : 4

12. 6738 cm^{2}

**Worksheet 3**

1. 64 cuboids

2. a. 960 m^{3} b. 7 cm

c. 2560 cm^{2} d. 726 cm^{2}

e. 729 cm^{3}

3. a. ii b. ii

c. i d. iii

4. a. ii b. i

c. iv d. iii

5. 8 cm; 512 cm^{3}

6. 1715 cm^{3}

7. 1,87,500 bricks

8. 10 cm

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