NCERT Solutions for Class 9 Maths Exercise 13.5 Chapter 13 Surface Areas and Volumes Term 2 CBSE Board exam - Future Study Point

# NCERT Solutions for Class 9 Maths Exercise 13.5 Chapter 13 Surface Areas and Volumes Term 2 CBSE Board exam

NCERT Solutions for Class 9 Maths Exercise 13.5 Chapter 13 Surface Areas and Volumes Term 2 CBSE Board exam are created here for helping the students in their preparation for the term 2 CBSE Board exam.All unsolved questions of the class 9 NCERT maths textbook exercise 13.5 chapter 5 Surface areas and Volumes are solved here by an experienced CBSE Maths teacher. Exercise 13.5 is based on the Surface areas and volumes of the cuboid and cubes. These NCERT Solutions for class 9 maths chapter 13 are useful for the competitive entrance exam also.

NCERT Solutions of class 9 maths is the most important study material in the preparation of the CBSE Board exam because chapter 13 -Surface areas and Volumes accommodate all the types of questions based on our real-life problems.

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## NCERT Solutions for Class 9 Maths  Chapter 13 Surface Areas and Volumes (Term 2 )CBSE Board exam

Class 9 Maths Exercise-13.1

Class 9 Maths Exercise-13.2

Class 9 Maths Exercise-13.3

Class 9 Maths Exercise -13.5

Class 9 Maths Exercise -13.7

Class 9 Maths Exercise -13.8

Class 9 Maths Exercise 13.9

NCERT Solutions Class 9 Maths-All Chapters

## NCERT Solutions for Class 9 Maths Exercise 13.5 Chapter 13 Surface Areas and Volumes Term 2 CBSE Board exam

Q1.A matchbox measures 4 cm×2.5cm×1.5cm. What will be the volume of a packet containing 12 such boxes?

Ans. The volume of a cuboid is =l×b×h

The dimensions of the matchbox are =4 cm×2.5cm×1.5cm

Therefore volume of the match box

=4 ×2.5×1.5

=15

The volume of the 12 match boxes

12 ×15 = 180

Volume of a packet containing 12  boxes is 180 cm³

Q2.A cuboidal water tank is 6m long, 5m wide and 4.5m deep. How many litres of water can it hold? (1 m3= 1000 l)

Ans.The length of a cuboidal tank is 6 m,breadth(b) 5 m and depth(h)4.5 m

The volume of the tank is

= l×b×h

=6×5×4.5

=135

Volume of water tank is 135 m³

1 m3= 1000 l

135 m³ = 135 ×1000=135000l

Hence volume of water tank is 135000l

Q3.A cuboidal vessel is 10m long and 8m wide. How high must it be made to hold 380 cubic metres of a liquid?

Ans.Let the height of  cuboidal vessel is h meter

The length(l) is 10 m and breadth(b) of the cuboidal vessel is 8m

The water holded in the vessel is 380 cubic metres

The volume of the cuboidal vessel = l ×b×h

l ×b×h = 380

10 ×8×h = 380

80× h = 380

h =380/80 =19/4 =4.75 m

Hence the height of  cuboidal vessel is 4.75 meter

Q4.Find the cost of digging a cuboidal pit 8m long, 6m broad and 3m deep at the rate of Rs 30 per m3.

Ans.Length (l) is 8 m,breadth(b) is 6 m and depth(h) is 3 m

Volume of the cuboidal pit

=l×b×h

=8×6×3

=144

Since the rate of digging the cuboidal pit is Rs 30 per m³

Therefore the cost of digging the cuboidal pit is  30×144=Rs 4420

Q5.The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m.

Ans.Let the breadth of the tank is b

The length (l) of a cuboidal tank is 2.5 m and depth(h)10 m

The volume of the tank is

= 2.5×b×10

=25b

Capacity of water tank is 50000 litre

1000 l = 1m³

50000 litre= 50000/1000 =50 m³

25b =50

b = 2

Therefore the breadth of the tank is 2 m

Q6.A village, having a population of 4000, requires 150 litres of water per head per day.

It has a tank measuring 20 m×15 m×6 m. For how many days will the water of this tank last?

Ans.Length (l) is 20 m,breadth(b) is 15 m and depth(h) is 6 m

Volume of the tank

=l×b×h

=20×15×6

=1800

Therefore volume of the tank is 1800 m³

The water consumption of the whole village per day =4000 ×150 = 600000 litres

1000 l = 1 m³

600000 /1000 =600 m³

Water of this tank last = Volume of the tank/The water consumption of the whole village per day

= 1800 /600 = 3

Water of this tank will last in 3 days

Q7.A godown measures 40 m×25m×15 m. Find the maximum number of wooden crates each

measuring 1.5m×1.25 m×0.5 m that can be stored in the godown.

Ans. The dimension of the godown =40 m×25m×15 m

Volume of godown =l ×b×h =40 ×25×15 =15000 m³

The dimension of the crate= 1.5m×1.25 m×0.5 m1.5×1.25 ×0.5

Volume of crate = 1.5×1.25 ×0.5 =0.9375 m³

The number of the crates accommodated in the godown

= Volume of godown/Volume of crate

= 15000/0.9375 =16000

The number of crates can be stored in the godown are 16000

Q8.A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.

Ans. Volume of the cube = a³,where a is the side of the cube

The volume of the cube having the side 12 cm =12³ =1728 m³

Let the side of the new cube is x

Volume of new 8 new cubes =8x³

8x³ = 1728

x³ = 1728/8 =216

x = 6

The ratio between surface area of the cubes

=6a²/6x²

=a²/x² =12²/6²=4/1

Hence the ratio between surface areas of the both cubes is 4 :1

Q9.A river 3m deep and 40m wide is flowing at the rate of 2km per hour. How much water will fall into the sea in a minute?

Ans. The depth (h) of the river is 3 m and its width is 40 m

The speed of the water in the river is 2 km/h =2000 m/60 minutes

Since volume of cuboid = l×b×h

The volume of water is flowing into the sea = 3×40×2000 =240000 m³/60 minutes

In 60 minutes the flow of water into the sea is = 240000 m³

In 1 minutes the flow of water into the sea is = 240000 /60 =4000 m³

Hence 4000 m³  water will fall into the sea in a minute

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