NCERT Solutions for class 10 Mathematics Chapter 13: Surface Areas and Volumes

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NCERT Solutions for Class 10 Mathematics Chapter 13 Surface Areas and Volumes are provided in this article. Some of the important topic in Surface areas and volumes chapter are:

Expected no of questions: 3 to 4 questions of total 6 to 7 marks

Download PDF: NCERT Solutions for Class 10 Mathematics Chapter 13 pdf

NCERT Solutions for Class 10 Mathematics Chapter 13

NCERT Solutions for Class 10 Mathematics Chapter 13 Surface area and volumes is given below.

Class 10 Mathematics Chapter 13 Surface Areas and Volumes – Important Topics

Surface area and volume are calculated for any three-dimensional geometrical shape. The surface area of any given object is the area or region occupied by the surface of the object. Whereas Volume is the amount of space available in an object.

In geometry, there are different shapes and sizes such as sphere, cube, cuboid, cone, cylinder, etc. Each shape has its surface area as well as volume. But in the case of two dimensional figures like square, circle, rectangle, triangle, etc., we can measure only the area covered by these figures and there is no volume available.

Some of the important formulas in this chapter include:

Cube:

The volume of cube = a³

Lateral Surface Area of cube = 4a²

Total Surface Area of cube = 6a²

Cuboid:

Volume of cuboid = l x b x h

Lateral Surface Area of cuboid = 2h(l+b)

Total Surface Area of cuboid = 2(lb + lh + bh)

Sphere:

Volume of sphere = (4/3) πr³

Curved Surface Area of sphere = 4πr²

Total Surface Area of sphere = 4πr²

Hemisphere:

Volume of hemisphere = (2/3) πr³

Curved Surface Area of hemisphere = 2πr²

Total Surface Area of hemisphere = 3πr²

Cone:

Volume of cone = (1/3) πr²h

Curved Surface Area of cone = πrl

Total Surface Area of cone = πr(r+l)

Cylinder:

Volume of cylinder = πr²h

Curved Surface Area of cone = 2πrh

Total Surface Area of cone = 2πrh + 2πr²

NCERT Solutions for Class 10 Maths Chapter 13 Exercises

NCERT Solutions for Class 10 Maths Chapter 13 Surface Areas and Volumes Exercises is given below.

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CBSE X Related Questions

1.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.
View Solution
2.
Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
View Solution
3.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.
View Solution
4.
Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.
View Solution
5.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$
View Solution
6.
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.
View Solution

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NCERT Solutions for class 10 Mathematics Chapter 13: Surface Areas and Volumes

Download PDF: NCERT Solutions for Class 10 Mathematics Chapter 13 pdf

NCERT Solutions for Class 10 Mathematics Chapter 13

Class 10 Mathematics Chapter 13 Surface Areas and Volumes – Important Topics

NCERT Solutions for Class 10 Maths Chapter 13 Exercises

CBSE X Related Questions

1.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

2.
Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

3.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

4.
Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

5.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

6.
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.

Similar Mathematics Concepts

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NCERT Solutions for class 10 Mathematics Chapter 13: Surface Areas and Volumes

Download PDF: NCERT Solutions for Class 10 Mathematics Chapter 13 pdf

NCERT Solutions for Class 10 Mathematics Chapter 13

Class 10 Mathematics Chapter 13 Surface Areas and Volumes – Important Topics

NCERT Solutions for Class 10 Maths Chapter 13 Exercises

CBSE X Related Questions

1.In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

2.Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

3.A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

4.Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

5.Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

6.PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

2.
Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

3.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

4.
Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

5.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

6.
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.