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Edited By Sumit Saini | Updated on Jul 12, 2022 02:27 PM IST

NCERT Solutions for Class 10 Maths exercise 13.3- We'll concentrate on solids conversion. For example, a cylinder-shaped candle can be melted and poured into a cubical container. The candle has been reshaped into a different shape. The volume of the candle remains constant, which is interesting to note. Students can determine that an object's volume remains constant even when it is converted from one solid shape to another as a consequence of this NCERT solutions Class 10 Maths chapter 13 exercise 13.3.

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- Surface Areas and Volumes Class 10 Maths Chapter 13 Exercise: 13.3
- Q9 A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled? Answer: Area of the cross-section of pipe is Speed of water is given to be = 3 km/hr Thus, the volume of water flowing through a pipe in 1 min. is Now let us assume that the tank will be completely filled after t minutes. Then we write : Hence the time required for filling the tank completely in 100 minutes.
- More About NCERT Solutions for Class 10 Maths Exercise 13.3 –
- Benefits of NCERT Solutions for Exercise 13.3 Class 10 Maths Chapter 13
- NCERT Solutions Subject Wise

NCERT solutions Class 10 Maths exercise 13.3- With the help of this exercise students understand that when Solids are remoulded and melted to change their shape, but their volume remains the same. With this understanding, students will be able to create equations.If students are asked to find the height of a shape in a question, they can simply equate the two equations where the volume is the same. They will be able to locate the missing dimension in this manner.

Along with Class 10 Maths chapter 13 exercise 13.3 the following exercises are also present.

Let us assume the height of the cylinder to be h.

Since the material is melted and recast thus its volume will remain the same.

So, Volume of sphere = Volume of obtained cylinder.

Hence the height of the cylinder is 2.74 cm.

According to the question, small spheres are melted and converted into a bigger sphere. Thus the sum of their volume is equal to the volume of the bigger sphere.

The volume of 3 small spheres = Volume of bigger sphere

Let us assume the radius of the bigger sphere is r.

Hence the radius of the sphere obtained is 12 cm.

According to the question, the volume of soil dug will be equal to the volume of the platform created.

Thus we can write :

The volume of soil dug = Volume of platform

Thus the height of the platform created is 2.5 m.

According to the question, the volume is conserved here :

The volume of soil dug out = Volume of the embankment made.

Let the height of the embankment is h.

Hence the height of the embankment made is 1.125 m.

Let the number of cones that can be filled with ice cream be n.

Then we can write :

The volume of a cylinder containing ice cream = n ( volume of 1 ice cream cone )

Hence the number of cones that can be filled is 10.

Let us assume the number of coins that need to be melted be n.

Then we can write :

The volume of n coins = Volume of cuboid formed.

Thus the required number of coins is 400.

According to question volume will remain constant thus we can write :

The volume of bucket = Volume of heap formed.

Let the radius of heap be r.

And thus the slant height will be

Hence the radius of heap made is 36 cm and its slant height is _{} .

Speed of water is: 10 Km/hr

And the volume of water flow in 1 minute is :

Thus the volume of water flow in 30 minutes will be :

Let us assume irrigated area be A. Now we can equation the expression of volumes as the volume will remain the same.

Thus the irrigated area is .

Area of the cross-section of pipe is

Speed of water is given to be = 3 km/hr

Thus, the volume of water flowing through a pipe in 1 min. is

Now let us assume that the tank will be completely filled after t minutes.

Then we write :

Hence the time required for filling the tank completely in 100 minutes.

There are many different shapes and sizes in geometry, such as the sphere, cube, cuboid, cone, cylinder, and so on. Each shape has a volume and a surface area. However, we can only measure the area covered by two-dimensional figures such as squares, circles, rectangles, triangles, and so on, and there is no volume available.

The total surface area includes the base(s) as well as the curved part. The area of only the curved part of a shape, excluding its base, is referred to as curved surface area (s). For shapes like a cylinder, it's also known as lateral surface area.

NCERT solutions for Class 10 Maths exercise 13.3-

Some important formulas are:

Volume of cone

Volume of cylinder

Volume of sphere

Volume of cuboid

**Also Read| **Surface Areas and Volumes Class 10 Notes

Exercise 13.3 Class 10 Maths is based on Conversion of Solid from One Shape to Another teaching us about shape conversion due to melting and recasting.

Class 10 Maths chapter 13 exercise 13.3 also covers the important concepts of exercise 13.2.

Class 10 Maths chapter 13 exercise 13.3 also contains concepts related to time value for objects to be filled or empty.

**Also, See:**

1. What is the core concept behind NCERT solutions for Class 10 maths exercise 13.4 ?

The core concept behind this exercise is the detailed study about Frustum of cones, and derivation for finding its volume, surface area etc.

2. What is a frustum?

The portion of a cone which remains after its upper part has been cut off by a plane parallel to its base is called frustum of a cone.

3. What is the formula for the volume of a frustum?

The portion of a cone which remains after its upper part has been cut off by a plane parallel to its base is called frustum of a cone.

4. What is the core concept for finding the volume of the frustum?

We simply take the volume of the bigger cone and then we subtract the volume of the smaller cone, thus we are left with the remaining volume which is the volume of the frustum

5. What is the formula for the total surface area of a frustum?

We simply take the volume of the bigger cone and then we subtract the volume of the smaller cone, thus we are left with the remaining volume which is the volume of the frustum

6. A drinking glass has an upper radius of 10 cm and lower radius of 8 cm with a height of 8 cm. The total volume of water we can fill the glass with is?

We simply take the volume of the bigger cone and then we subtract the volume of the smaller cone, thus we are left with the remaining volume which is the volume of the frustum

7. A large container pipe has two circular openings with radius 12 m and 15 m. Its walls are to be painted with a paint of 0.001 m thick. Then the volume of paint required is when the height is 4m?

8. A frustum has a radius of 10 m and 20 m with a height of 24m find its total surface area?

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