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

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

Edited By Vishal kumar | Updated on Oct 16, 2023 10:59 AM IST

## NCERT Solutions for Class 9 Maths Exercise 13.5 Chapter 13 Surface Areas and Volumes- Download Free PDF

NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Exercise 13.5- Prepare effectively for your annual exams with NCERT solutions for class 9 Maths Chapter 13 exercise 13.5 on Surface Areas and Volumes. These 9th class maths exercise 13.5 answers, thoughtfully created by experienced subject-matter experts at Careers360, align seamlessly with the NCERT syllabus and CBSE guidelines. Exercise 13.5 class 9 maths serve as a valuable resource for students, offering comprehensive answers to assist with homework, assignments, and quick reference, ensuring a strong foundation in geometry and 3D shapes.

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.

The class 9 maths ex 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.

**As per the CBSE Syllabus for 2023-24, this chapter has been restructured and is now identified as Chapter 11.

## Download the PDF of NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Exercise 13.5

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

Given,

Dimensions of a matchbox = $\small 4\hspace{1mm}cm\times 2.5\hspace{1mm}cm\times 1.5\hspace{1mm}cm$

We know,

The volume of a cuboid = $l\times b \times h$

$\small \therefore$ The volume of a matchbox= $\small (4 \times2.5\times 1.5)\ cm^3 = 15\ cm^3$

$\small \therefore$ Volume of 12 such matchboxes = $\small (15\times12)\ cm^3 = 180\ cm^3$

Therefore, the volume of a packet containing 12 matchboxes is $\small 180\ cm^3$

Given,

Dimensions of the cuboidal water tank = $6\ m \times5\ m\times 4.5\ m$

We know,

Volume of a cuboid = $l\times b \times h$

$\small \therefore$ Volume of the water tank = $\small (6 \times5\times 4.5)\ m^3 = 135\ m^3$

We know,

$\small 1\hspace{1mm}m^3=1000\hspace{1mm}l$

$\small \therefore$ Volume of water the tank can hold = $\small (135\times1000) = 135000\ litres$

Let the height of the vessel be $h\ m$

Dimensions of the cuboidal water tank = $10\ m \times8\ m\times h\ m$

We know,

The volume of a cuboid = $l\times b \times h$

$\small \therefore$ The volume of the water tank = $\small (10 \times8\times h)\ m^3 = 80h\ m^3$

According to question,

$\small \\ \Rightarrow h= \frac{380}{80} = 4.75$

Therefore, the required height of the vessel is $\small 4.75\ m$

Given,

Dimensions of the cuboidal pit = $8\ m\times 6\ m\times 3\ m$

We know , Volume of a cuboid = $l\times b\times h$

$\therefore$ Volume of the cuboidal pit = $(8\times 6\times 3\) = 144\ m^3$

Now, Cost of digging $\small 1\ m^3$ = Rs. 30

$\therefore$ Cost of digging $144\ m^3$ = $Rs.(144\times30)$

$= Rs.4320$

Given,

Length of the tank = $\small l = 2.5\hspace{1mm}m$

Depth of the tank = $h = 10\ m$

Let the breadth of the tank be $\small b\ m$

We know, Volume of a cuboid = $l\times b\times h$

$\therefore$ The volume of the cuboidal tank = $(2.5\times b\times 10) = 25b\ m^3$

We know, $1\ m^3 = 1000\ litre$

$\therefore$ $25b\ m^3 = 50000\ litre = 50\ m^3$

$\\ \Rightarrow 25b = 50 \\ \Rightarrow b = 2\ m$

Therefore, the breadth of the tank is $2\ m$

Given,

Dimensions of the tank = $\small 20\hspace{1mm}m\times 15\hspace{1mm}m\times 6\hspace{1mm}m$

4000 people requiring 150 litres of water per head per day

The total volume of water required = $4000\times150 = 600000\ litres$

Let the number of days the water will last be $n$

We know,

The volume of a cuboid = $l\times b \times h$

$\small \therefore$ The volume of the water tank = $\small (20 \times15\times 6)\ m^3 = 1800\ m^3 = 1800000\ litres$

According to question,

$\small n\times600000 = 1800000$

$\small \\ \Rightarrow n= 3$

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

Given,

Dimensions of the godown = $\small 40\hspace{1mm}m\times 25\hspace{1mm}m\times 15\hspace{1mm}m$

Dimension of each wooden crate = $\small 1.5\hspace{1mm}m\times 1.25\hspace{1mm}m\times 0.5\hspace{1mm}m$

We know , Volume of a cuboid = $l\times b\times h$

$\therefore$ Volume of the godown = $(40\times 25\times 15)\ m^3$

$\therefore$ Volume of the each crate= $(1.5\times 1.25\times 0.5)\ m^3$

Let number of wooden crates be $n$

$\therefore$ Volume of $n$ wooden crates = Volume of the godown

$n\times(1.5\times 2.5\times 0.5)\ m^3 = (40\times 25\times 15)\ m^3$

$\\ \Rightarrow n = \frac{40\times 25\times 15}{1.5\times 1.25\times 0.5} \\ \\ \Rightarrow n = 80\times 20\times 10 = 16000$

This is an important question.

Given,

Side of a solid cube = $l = 12\ cm$

We know, the volume of a cube of side $l$ = $l^3$

$\therefore$ The volume of the given cube = $12^3\ cm^3$

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

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

$\Rightarrow (8\times a^3)\ cm^3 = 12\ cm^3$

$\\ \Rightarrow a^3 = \frac{12}{8} \\ \Rightarrow a^3 = \left (\frac{12}{2} \right ) \\ \Rightarrow a = 6\ cm$

Therefore, the side of the new cube is $6\ cm$

Now, we know,

The surface area of a cube of side $l$ = $6l^2$

$\therefore$ The ratio between their surface areas $= \frac{Surface\ area\ of\ bigger\ cube}{Surface\ area\ of\ a\ smaller\ cube}$

$\\ = \frac{6l^2}{6a^2} \\ = \left (\frac{l}{a} \right )^2 \\ = \left (\frac{12}{6} \right )^2 \\ = 4$

Therefore, the ratio of their surface areas is $4:1$

Given,
Rate of water flow = $2\ km\ per\ hour$
$= \frac{2\times1000}{60}\ m/min$
$= \frac{100}{3}\ m/min$
Depth of river, $h = 3\ m$
Width of the river, $b= 40\ m$
The volume of water flowing in 1 min = $Rate\ of\ flow \times Cross\ sectional\ area$

$= \frac{100}{3}\times40\times3$

$= 4000\ m^3$

Therefore, water falling into the sea in a minute = $4000\ m^3$

## 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.

• 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.

## Key Features of Class 9 Maths Chapter 13 Exercise 13.5

• Comprehensive Coverage: This class 9 maths ex 13.5 covers advanced topics related to surface areas and volumes of solids, including cones, cylinders, and spheres.
• Expert-Crafted Solutions: The 9th class maths exercise 13.5 answers are created by subject matter experts, providing clear, step-by-step explanations to help students grasp complex concepts.
• CBSE 2023-24 Syllabus: The exercise 13.5 class 9 maths aligns with the CBSE 2023-24 syllabus, ensuring that students are well-prepared for their exams.
• Homework and Assignment Support: These class 9 ex 13.5 solutions serve as a valuable resource for completing homework and assignments.
• Quick Reference Guide: Students can use these solutions as a quick reference guide to reinforce their understanding of geometry and 3D shapes.

Also, See:

## NCERT Solutions of Class 10 Subject Wise

1. Define cuboid , as per the NCERT solutions for Class 9 Maths chapter 13 exercise 13.5 .

A cuboid is a three-dimensional object bounded by six rectangular planes, each of which has a different magnitude of length, breadth, and height, as per NCERT solutions for Class 9 Maths chapter 13 exercise 13.5.

2. The volume of the cuboid is ________

The volume of the cuboid is lbh

3. The volume of the cube is ______

The volume of the cube is a3

4. Define the volume of the cuboid, according to NCERT solutions for Class 9 Maths chapter 13 exercise 13.5 .

The total space occupied by the cuboid in a three-dimensional space is known as the volume of the cuboid, according to NCERT solutions for Class 9 Maths chapter 13 exercise 13.5 .

5. Volume of a cube of sides m is ______

Volume of a cube of sides m is  m3 .

6. The volume of a cube whose edge 3 m is ________

The volume of the cube whose edge a is a3

The volume of the cube whose edge 3 is 33=81 m3

7. Define the term 'cube' .

A cube is a three-dimensional shape with six faces, eight vertices, and twelve edges.

8. The volume of the cuboid can be calculated by using ________

The volume of the cuboid can be calculated by using the dimensions.

9. What are the dimensions of the cuboid?

The dimensions of the cuboid are length , breadth and height.

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