# NCERT Solutions for Exercise 13.5 Class 9 Maths Chapter 13 - Surface Area and Volumes

NCERT Solutions for Class 9 Maths exercise 13.5 deal with the concept of volume of the cuboid. The cuboid is a three-dimensional figure bounded by six rectangular planes, each of which has a different magnitude of length, width, and height. It has eight vertices and twelve edges, and its opposite faces are always equal. The total space occupied by the cuboid in a three-dimensional space is known as the volume of the cuboid in exercise 13.5 Class 9 Maths. In other words, The amount of space occupied by the shape of a cuboid is known as the volume of the cuboid. The volume of the cuboid can be calculated by using the dimensions such as length, width and height.

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The NCERT solutions for Class 9 Maths exercise 13.5 also focused on the volume of the cube. A three-dimensional shape which has six faces, eight vertices and twelve edges is known as a cube. The volume of a cube is a3 where a is the edge of the cube. NCERT solutions for Class 9 Maths chapter 13 exercise 13.5 consists of 9 questions regarding the volume of the cuboid. The concepts related to the volume of the cuboid and cube are well explained in this NCERT book Class 9 Maths chapter 13 exercise 13.5. Along with NCERT syllabus Class 9 Maths chapter 13 exercise 13.5 the following exercises are also present.

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• Surface Area and Volumes Exercise 13.1
• Surface Area and Volumes Exercise 13.2
• Surface Area and Volumes Exercise 13.3
• Surface Area and Volumes Exercise 13.4
• Surface Area and Volumes Exercise 13.6
• Surface Area and Volumes Exercise 13.7
• Surface Area and Volumes Exercise 13.8
• Surface Area and Volumes Exercise 13.9

## Surface Area and Volumes Class 9 Chapter 13 Exercise: 13.5

Q1 A matchbox measures . What will be the volume of a packet containing 12 such boxes?

Given,

Dimensions of a matchbox =

We know,

The volume of a cuboid =

The volume of a matchbox=

Volume of 12 such matchboxes =

Therefore, the volume of a packet containing 12 matchboxes is

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

Given,

Dimensions of the cuboidal water tank =

We know,

Volume of a cuboid =

Volume of the water tank =

We know,

Volume of water the tank can hold =

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

Let the height of the vessel be

Dimensions of the cuboidal water tank =

We know,

The volume of a cuboid =

The volume of the water tank =

According to question,

Therefore, the required height of the vessel is

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

Given,

Dimensions of the cuboidal pit =

We know , Volume of a cuboid =

Volume of the cuboidal pit =

Now, Cost of digging = Rs. 30

Cost of digging =

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 and 10 m.

Given,

Length of the tank =

Depth of the tank =

Let the breadth of the tank be

We know, Volume of a cuboid =

The volume of the cuboidal tank =

We know,

Therefore, the breadth of the tank is

Q6 A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring . For how many days will the water of this tank last?

Given,

Dimensions of the tank =

4000 people requiring 150 litres of water per head per day

The total volume of water required =

Let the number of days the water will last be

We know,

The volume of a cuboid =

The volume of the water tank =

According to question,

Therefore, the water in the tank will last for 3 days.

Q7 A godown measures . Find the maximum number of wooden crates each measuring that can be stored in the godown.

Given,

Dimensions of the godown =

Dimension of each wooden crate =

We know , Volume of a cuboid =

Volume of the godown =

Volume of the each crate=

Let number of wooden crates be

Volume of wooden crates = Volume of the godown

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.

This is an important question.

Given,

Side of a solid cube =

We know, the volume of a cube of side =

The volume of the given cube =

Now, the cube is cut into 8 equal cubes of side (let)

The total volume of these 8 cubes = Volume of the bigger cube

Therefore, the side of the new cube is

Now, we know,

The surface area of a cube of side =

The ratio between their surface areas

Therefore, the ratio of their surface areas is

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

Given,
Rate of water flow =

Depth of river,
Width of the river,
The volume of water flowing in 1 min =

Therefore, water falling into the sea in a minute =

## More About NCERT Solutions for Class 9 Maths Exercise 13.5

The NCERT solutions for Class 9 Maths exercise 13.5 mainly focused on the volume of the cuboid. The volume of the cuboid is nothing but the space occupied by its dimensions which is given by the product of its length, breadth and its height. That is V=lbh. In order to find the volume of the cuboid, first, we need to check the dimensions such as length, breadth and height of the given cuboid. Then we need to check whether all the dimensions such as length, breadth and height are of the same unit or else we need to convert them into the same units. After making the units the same for all the dimensions then we need to multiply length, breadth and height together. Thus the obtained value is the volume of the cuboid which should be written in cubic units. The formulas of calculating volume of the cuboid and cube are well discussed in NCERT solutions for Class 9 Maths exercise 13.5.

Also Read| Surface Areas And Volumes Class 9 Notes

## Benefits of NCERT Solutions for Class 9 Maths Exercise 13.5 :

• NCERT solutions for Class 9 Maths exercise 13.5 helps us to prepare well for our second term as well as competitive examinations also helpful for us to do our homework and aids as an instant reference guide.

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• By solving the NCERT solution for Class 9 Maths chapter 13 exercise 13.5 exercises, it helps to know the easy way to solve the problems and helps us to analyse the situation and apply the formula correctly and also improve our efficiency and speed in solving the problems.

• Exercise 13.5 Class 9 Maths, helps us to determine the volume of the cuboid and also in finding the length and breadth of the cuboid by applying the formula of the volume.

Also, See:

• NCERT Solutions for Class 9 Maths Chapter 13 – Surface Area and Volumes

• NCERT Exemplar Solutions Class 9 Maths Chapter 13 – Surface Area and Volumes

## NCERT Solutions of Class 10 Subject Wise

• NCERT Solutions for Class 9 Maths

• NCERT Solutions for Class 9 Science