NCERT Solutions of class 10 maths Exercise 13.3-Surface areas and Volumes

NCERT Solutions of class 10 maths Exercise 13.3 of the chapter 13-Surface areas and Volumes-Here NCERT Solutions of the exercise 13.3 are the Solutions of the chapter ‘Surface areas and Volumes’ of the NCERT maths coursebook of class 10 endorsed by CBSE a reputed Board of India for school education.All questions of exercise 13.3 are solved by an expert of maths in a step-by-step way, so everyone would comprehend the profundity of the idea of maths.

There are a variety of questions in chapter- 13 based on surface areas and volumes of compound figures made of cubes, cuboids, cylinders, cones, and spheres. In exercise 13.3, the questions based on evaluation of the volumes, height, and radius of solids when one solid is melted and recast into another solid. In this exercise for the evaluation of physical quantities like height, radius, surface areas, and volume, you need to keep in mind the following points.

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In the case when one metallic object is melted and recast into another type of article then the volume of both will be the same.
In the case when the earth is taken out from a well to be dug out and something is made by the earth taken out from the well then the volume of the well is equivalent to the thing to be made.
In a question, if you are given the speed of the water (distance/unit time)then the volume of water streamed in per unit time =depth ×height ×speed.

NCERT Solutions Class 10 Science from chapter 1 to 16

The questions of exercise 13.3 are very important for your board examination of 2020-21. We likewise have highlighted the questions which are important and most important, so that you could pay attention to those questions.

NCERT Solutions of class 10 maths

Chapter 1-Real number	Chapter 9-Some application of Trigonometry
Chapter 2-Polynomial	Chapter 10-Circles
Chapter 3-Linear equations	Chapter 11- Construction
Chapter 4- Quadratic equations	Chapter 12-Area related to circle
Chapter 5-Arithmetic Progression	Chapter 13-Surface areas and Volume
Chapter 6-Triangle	Chapter 14-Statistics
Chapter 7- Co-ordinate geometry	Chapter 15-Probability
Chapter 8-Trigonometry

CBSE Class 10-Question paper of maths 2021 with solutions

CBSE Class 10-Half yearly question paper of maths 2020 with solutions

CBSE Class 10 -Question paper of maths 2020 with solutions

CBSE Class 10-Question paper of maths 2019 with solutions

NCERT Solutions of class 10 maths Exercise 13.3 -Surface areas and Volumes

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Q1.A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.(Imp)

Ans.We are given the radius of the sphere = 4.2 cm

Radius of the cylinder = 6 cm

Let the height of cylinder = h

The volume of sphere = Volume of cylinder

Volume of sphere = and Volume of cylinder is =

h = 2.74

Hence the height of the cylinder = 2.74 cm

Q2.Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.(Imp)

Ans. We are given the radii of three metalic spheres 6 cm, 8 cm and 10 cm respectively

Sum of the volumes of metalic spheres = Volume of a single solid sphere

The volume of sphere =

Let the radius of the single solid sphere = r

r ³ = 6³ + 8³ + 10³

r³ = 216 + 512+1000

r³ = 1728

Hence the radius of single solid sphere is 12 cm

Q3.A 20 m deep well with a diameter of 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.(Very Imp)

Ans. We are given the depth of the well, h = 20 m, radius, r of the well = 7/2= 3.5 cm

Let the height of the platform made by the earth taken out from the well =H

The shape of well is the shape of a cylinder

The volume of well = The volume of the earth taken out from the well= Volume of the platform = πr²h =22/7 ×3.5²×20 =22×0.5×3.5×20 = 770 m³

The volume of plateform = Length ×Breadth × Height = 22 × 14 × H

Therefore

22 ×14 H = 770

H = 2.5 m

Hence the height of the plateform = 2.5 m↓

Q4.A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.(Most Imp)

Ans.Let the height of the embankment= H

Radius of well = 3/2 = 1.5 m, height, h =14 m

The volume of well = The volume of the earth taken out from the well= Volume of the embankment

Volume of well =πr²h =π(1.5)²14

Outer radius of embankment =1.5 +4 = 5.5 m

Inner radius of embankment = 1.5 m

Volume of embankment =π(5.5)²H – π(1.5)²H=πH(5.5²- 1.5²)=πH(30.25 -2.25)=28πH

28πH = π(1.5)²14

28H =2.25×14

H = 2.25/2 =1.125

Hence the height of embankment is 1.125 m

Q5. A container shaped like right circular cylinder having diameter 12 cm and height 15 cm is full of ice-cream .The ice-cream is to be filled into cones of height 12 cm and diameter 6 cm ,having hemisperical shape on the top .Find the number of such cones which can be filled with ice-cream.(Most Imp)

Ans.

We are given diameter of right circular cylinder= 12 cm,so radius,r = 12/2 = 6 cm

Height of the cylinder ,h =15 cm

Volume of cylinder = πr²h = π(6)²15 =540π cm³

The volume of ice-cream = Volume of cone + Volume of hemisphere

The height,h of the cone =12 cm and radius of cone and hemisphere,r= 6/2= 3 cm

Volume of cone =

= 3π ×12 = 36π

Volume of hemisphere =

= 2π× 9 = 18π

∴ The volume of ice-cream = 36π + 18π =54 π cm³

Number of ice-cream cones to be filled

Hence the number of cones to be filled are 10

Q6.How many silver coins, 1.75 cm in diameter and of thickness 2 mm,must be meted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm ?(Imp)

Ans.Let number of coins to be formed = n

Radius of coins,r = 1.75/2 = 0.875 cm and thickness,h=2 mm = 0.2 cm

Volume of coin = πr²h

=4.4 × 0.125×0.875=0.48125 cm³

Volume of cuboid = Length× Breadth ×Height =5.5 cm × 10 cm × 3.5 cm =192.5 cm³

Number of coins to be melted

= 400

Hence the number of coins to be melted are 400

Q7. A cylindrical bucket ,32 cm high and with radius of base 18 cm ,is filled with sand .This bucket is emptied on the ground and a conical heap of sand is formed .If the height of conical heap is 24 cm,find the radius and slant height of the heap. (Very Imp)

Ans. The volume of the bucket = Volume of conical heap

We are given the height of the cylindrical bucket,h = 32 cm and radius of base, = 18 cm

Volume of cylndrical bucket = πr²h = π(18)²32

The height of conical heap =24 cm

Volume of conical heap =

The volume of the bucket = Volume of conical heap

r² = (18 ×18× 4)

r²=9 ×2×9×2×4

r = 9×2×2= 36 cm

Hence radius of the conical heap = 36 cm

Slant height of the conical heap,l =√(r² +h²) = √(36² + 24²)=√(1296 +576)=√(1872)=12√13 cm

Q8.Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?(Most Imp)

Ans.Let area to be irrigated A in time 30 minutes=30 ×60=1800 seconds

Standing water in the area= 8 cm= o.08 m

We are given width of canal is =6 m and depth=1.5 m

The speed of water =10 km/h = (10×1000)/(60×60) =25/9 m/s

Volume of water flowed in the area in per second =Width ×Depth ×Speed of water=6×1.5×25/9=2×0.5×25=25 m³/s

In 30 minutes (1800 s) the water flowed in the area =25 ×1800=45000 m³

The volume of standing water in 30 minutes = A×h =0.08 A

0.08 A = 45000

A = 45000/0.08= 562500 m²

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?(Most Imp)

Ans. We are given the diameter of the pipe = 20 cm = 0.20 m, so its radius =.20/2=0.10 m

The speed of water in the pipe = 3 km/h = 3000/(60×60) =3000/3600=(5/6) m/s

The volume of water flowed per second through the pipe=πr²h=π(0.10)²×5/6=0.05π/6 m³/s

The diameter of cylindrical tank = 10 m,so its radius =10/2= 5m

Depth(h) of the tank = 2 m

Volume of the tank =πr²h =π(5²)×2= 50π m³

Time taken by the pipe in filling the tank =(Volume of tank)/(Volume of water flowed per second inside the pipe) = 50π /(0.05π/6) =300/0.05= 6000 seconds=100 minutes= 1h 40 minutes

Science and Maths NCERT Solutions for Class 9,10,11 and 12

NCERT Solutions of class 9 maths

Chapter 1- Number System	Chapter 9-Areas of parallelogram and triangles
Chapter 2-Polynomial	Chapter 10-Circles
Chapter 3- Coordinate Geometry	Chapter 11-Construction
Chapter 4- Linear equations in two variables	Chapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s Geometry	Chapter 13-Surface Areas and Volumes
Chapter 6-Lines and Angles	Chapter 14-Statistics
Chapter 7-Triangles	Chapter 15-Probability
Chapter 8- Quadrilateral

NCERT Solutions of class 9 science

Chapter 1-Matter in our surroundings	Chapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?	Chapter 10- Gravitation
Chapter3- Atoms and Molecules	Chapter 11- Work and Energy
Chapter 4-Structure of the Atom	Chapter 12- Sound
Chapter 5-Fundamental unit of life	Chapter 13-Why do we fall ill ?
Chapter 6- Tissues	Chapter 14- Natural Resources
Chapter 7- Diversity in living organism	Chapter 15-Improvement in food resources
Chapter 8- Motion	Last years question papers & sample papers

CBSE Class 9-Question paper of science 2020 with solutions

CBSE Class 9-Sample paper of science

CBSE Class 9-Unsolved question paper of science 2019

NCERT Solutions of class 10 maths

Chapter 1-Real number	Chapter 9-Some application of Trigonometry
Chapter 2-Polynomial	Chapter 10-Circles
Chapter 3-Linear equations	Chapter 11- Construction
Chapter 4- Quadratic equations	Chapter 12-Area related to circle
Chapter 5-Arithmetic Progression	Chapter 13-Surface areas and Volume
Chapter 6-Triangle	Chapter 14-Statistics
Chapter 7- Co-ordinate geometry	Chapter 15-Probability
Chapter 8-Trigonometry

CBSE Class 10-Question paper of maths 2021 with solutions

CBSE Class 10-Half yearly question paper of maths 2020 with solutions

CBSE Class 10 -Question paper of maths 2020 with solutions

CBSE Class 10-Question paper of maths 2019 with solutions

NCERT solutions of class 11 maths

Chapter 1-Sets	Chapter 9-Sequences and Series
Chapter 2- Relations and functions	Chapter 10- Straight Lines
Chapter 3- Trigonometry	Chapter 11-Conic Sections
Chapter 4-Principle of mathematical induction	Chapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbers	Chapter 13- Limits and Derivatives
Chapter 6- Linear Inequalities	Chapter 14-Mathematical Reasoning
Chapter 7- Permutations and Combinations	Chapter 15- Statistics
Chapter 8- Binomial Theorem	Chapter 16- Probability

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

NCERT solutions of class 12 maths

Chapter 1-Relations and Functions	Chapter 9-Differential Equations
Chapter 2-Inverse Trigonometric Functions	Chapter 10-Vector Algebra
Chapter 3-Matrices	Chapter 11 – Three Dimensional Geometry
Chapter 4-Determinants	Chapter 12-Linear Programming
Chapter 5- Continuity and Differentiability	Chapter 13-Probability
Chapter 6- Application of Derivation	CBSE Class 12- Question paper of maths 2021 with solutions
Chapter 7- Integrals
Chapter 8-Application of Integrals