Surface Area and Volume Class 9 Worksheet 1 with Answers
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 cm3
b.
Side of a cube = 5 cm ii. 384 cm2
c.
Side of a cube = 8 cm iii.
34 cm2
d.
Length = 2 cm, breadth = 1.5 cm, height = 4 cm iv.
13 m2
e.
Length = 3 m, breadth = 25 cm, height = 2 m v.
120 cm3
3.
The total surface area of a cube is 2166 cm2.
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 m3. What
are the dimensions of the cuboid?
6.
If the surface area of a cube is 54 cm3.
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 m3 of air?
8.
The surface area of a cuboid is 264 cm2.
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 m3.
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 cm3. 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 cm2.
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 cm2.
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 with Answers
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 11/2
times its height. The cost of whitewashing the walls at the rate of ₹ 1.60 per
m2 is ₹ 179.20. Find the cost of tiling the floor at the rate of ₹ 6.75 per m2.
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 cm3 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 m3, how many bags can be
stored in the granary?
9. A cuboid has total surface area 40 m2 and its lateral
surface area is 26 m2. Find the area of its base.
10.
The total surface area of a cuboid is 7502 cm2.
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 with Answers
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 cm3, 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 cm3. 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. x2
ii. x3
iii. 4x
iv. 4x2
b.
Volume of a tank with a square base area 4900 cm2 and height 60 cm is
i. 294 cm2
ii. 294000 cm3
iii. 29.4 cm3
iv. 4200 cm
c.
Volume of a cube is 27000000 cm3, hence its volume in m3 is
i. 27 m3
ii. 270 m3
iii. 27000 m3
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 cm2
ii. 216 cm2
iii. 268 cm2
iv. 80 cm2
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 cm3
b.
If surface area of a cube is 294 cm2, then its volume is ii. 5 m
c.
Volume of a cube is 3375 cm3, then its edge is iii. 1000000
d. 1 m3 in
cm3 is iv.
15 cm
5.
Lateral surface area of a cube is 256 cm2.
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 cm2?
ANSWERS
Worksheet 1
1. a. 89,746.5
cm3
b. 15,253.5 cm3
2. a. v b. i
c. ii d. iii
e. iv
3. 6859 cm3
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 cm2
12. 460.8 m3
13. 3.5 cm; 42.875 cm3
14. a. 9.342 cm b. 12.11 cm
15. ₹ 2400 16. 560 cm3
Worksheet 2
1. 3 : 2 2. ₹ 324
3. 8V 4. ₹ 640
5. 350 cm3 6. 2 m
7. 4 m × 6 m × 8 m
8. 240 bags 9. 7 m2
10. 6050 cm2
11. 6 cm; 1 : 4
12. 6738 cm2
Worksheet 3
1. 64 cuboids
2. a. 960 m3 b. 7 cm
c. 2560 cm2 d. 726 cm2
e. 729 cm3
3. a. ii b. ii
c. i d. iii
4. a. ii b. i
c. iv d. iii
5. 8 cm; 512 cm3
6. 1715 cm3
7. 1,87,500 bricks
8. 10 cm
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