# rd sharma class 10 surface area and volume solutions

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## RD Sharma Solutions for Class 10 Maths Chapter 16 Surface Areas And Volumes

RD Sharma Solutions for Class 10 Maths Updated (2022-23) Chapter 16 Surface Areas And Volumes provide in-depth knowledge to find surface areas and volumes of different solids and their combinations.

RD Sharma SolutionsClass 10Chapter 16 Surface Area And Volume

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## RD Sharma Solutions for Class 10 Maths Chapter 16 Surface Areas And Volumes

RD Sharma Solutions for Class 10 Maths Chapter 16 Surface Areas And Volumes RD Sharma Solutions Class 10 Maths Chapter 16 – Download Free PDF Updated for 2022 – 2023

**RD Sharma Solutions for Class 10 Maths Chapter 16 – Surface Areas And Volumes**are provided here to enhance knowledge of the covered concepts and score good marks in exams. Applications of Mathematics in everyday life are enormous. One such application is to find the surface areas and volumes of different solids and their combinations. This Chapter is one of the important chapters in Class 10 Mathematics. Professional teachers developed the RD Sharma Solutions for students to strengthen conceptual knowledge and solve problems with competence.

**Chapter 16- Surface Areas And Volumes**contains three exercises. Students can find precise step wise answers for these exercise problems in RD Sharma Solutions for Class 10 Maths. Subject matter experts have developed these solutions to match the standards of all levels of students. In this chapter, students will be solving problems on finding surface areas and volumes of combinations of solids like a cuboid, cube, right circular cylinder, right circular cone, sphere, hemisphere, and frustum of a cone.

Chapter 16 Surface Areas And Volumes

Exercise

## Download the PDF of RD Sharma Solutions For Class 10 Maths Chapter 16 Surface Areas And Volumes here

## RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Revision Exercise

## RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Revision Exercise

June 7, 2018 by Prasanna

## RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Revision Exercise

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Revision Exercise

**Other Exercises**

RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.1

RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.2

RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Ex 14.3

RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Revision Exercise

RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes VSAQS

RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes MCQS

**Question 1.**

**A metallic sphere 1 dm in diameter is beaten into a circular sheet of uniform thickness equal to 1 mm. Find the radius of the sheet.**

**Solution:**

Diameter of a sphere = 1 dm = 10 cm

∴ Radius (r) = ( 10 2 ) = 5 cm

Volume of metal used in the sphere =

( 4 3 ) πr³

RD Sharma Class 10 Solutions Chapter 14 Surface Areas and Volumes Revision Exercise

**Question 2.**

**Three solid spheres of radii 3,4 and 5 cm respectively are melted and converted into a single solid sphere. Find the radius of this sphere.**

**Solution:**

Radius of first sphere (r1) = 3 cm

**Question 3.**

**A spherical shell of lead, whose external diameter is 18 cm, is melted and recast into a right circular cylinder, whose height is 8 cm and diameter 12 cm. Determine the internal diameter of the shell.**

**Solution:**

Diameter of the cylinder = 12 cm

∴ Radius (r1) = ( 12 2 ) = 6 cm Height (h) = 8 cm

∴ Volume = πr1²h = π(6)² x 8 cm³

= π x 36 x 8 = 288π cm³

Now volume of metal used in spherical shell = 288π cm

External diameter = 18 cm 18

∴ External radius (R) =

( 18 2 ) = 9 cm

Let r be the internal radius, then

Volume of the metal =

( 4 3 ) π (R³ – r³ )

**Question 4.**

**A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread all around it to a width of 7.5 m to form an embankment. Find the height of the embankment.**

**Solution:**

Diameter of two well = 10 m

∴ Radius (r) = ( 10 2 ) = 5 m Depth (h) = 8.4 m

∴ Volume of earth dug out = πr²h

**Question 5.**

**In the middle of a rectangular field measuring 30 m x 20 m, a well of 7 m diameter and 10 m depth is dug. The earth so removed is evenly spread over the remaining part of the field. Find the height through which the level of the field is raised.**

**Solution:**

Diameter of well = 7 m

∴ Radius (r) = ( 7 2 ) m Depth (h) = 10 m

∴ Volume of earth dug out = πr²h

**Question 6.**

**The inner and outer radii of a hollow cylinder are 15 cm and 20 cm, respectively. The cylinder is melted and recast into a solid cylinder of the same height. Find the radius of the base of new cylinder.**

**Solution:**

Inner radius of hollow cylinder (r) = 15 cm

Outer radius (R) = 20 cm

Let h be the height of the hollow cylinder,

Then volume of metal used = πR (R² – r²)

= πh (20²- 15²) cm³

= πh (400 – 225) cm³

= 175 πh cm³

Volume of the new cylinder = 175nh cm³

Height = h

Let R be the radius of new cylinder,

then πR²h = 175 πh ⇒ R²= 175 ⇒ R = 175 − − − √ = 13.2 ∴ Radius = 13.2 cm

**Question 7.**

**Two cylindrical vessels are filled with oil. Their radii are 15 cm, 12 cm and heights 20 cm, 16 cm respectively. Find the radius of a cylindrical vessel 21 cm in height, which will just contain the oil of the two given vessels.**

**Solution:**

Radius of first cylinder (r1) = 15 cm

and radius of second cylinder (r2) = 12 cm

Height of the first cylinder (h1) = 20 cm

## RD Sharma solutions for Class 10 Maths chapter 14

Get free RD Sharma Solutions for Class 10 Maths Chapter 14 Surface Areas and Volumes solved by experts. Available here are Chapter 14 - Surface Areas and Volumes Exercises Questions with Solutions and detail explanation for your practice before the examination

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## RD Sharma solutions for Class 10 Maths chapter 14 - Surface Areas and Volumes [Latest edition]

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## Chapter 14: Surface Areas and Volumes

Exercise 14.1Exercise 14.2Exercise 14.3Exercise 14.3Exercise 14.4Exercise 14.5

EXERCISE 14.1 [PAGES 27 - 32]

### RD Sharma solutions for Class 10 Maths Chapter 14 Surface Areas and Volumes Exercise 14.1 [Pages 27 - 32]

Exercise 14.1 | Q 1 | Page 27

How many balls each of radius 1cm can be made from a solid sphere of lead of radius

8cm? VIEW SOLUTION

Exercise 14.1 | Q 2 | Page 27

How many spherical bullets each of 5cm in diameter can be cast from a rectangular block of metal 11 dm x 1m x 5 dm?

VIEW SOLUTION

Exercise 14.1 | Q 3 | Page 27

A spherical ball of radius 3cm is melted and recast into three spherical balls. The radii of the two of balls are 1.5cm and 2cm . Determine the diameter of the third ball?

VIEW SOLUTION

Exercise 14.1 | Q 4 | Page 27

2.2 Cubic dm of grass is to be drawn into a cylinder wire 0.25cm in diameter. Find the length of wire?

VIEW SOLUTION

Exercise 14.1 | Q 5 | Page 28

What length of a solid cylinder 2cm in diameter must be taken to recast into a hollow

cylinder of length 16cm, external diameter 20cm and thickness 2.5mm?

VIEW SOLUTION

Exercise 14.1 | Q 6 | Page 28

A cylindrical vessel having diameter equal to its height is full of water which is poured into two identical cylindrical vessels with diameter 42cm and height 21cm which are filled completely. Find the diameter of cylindrical vessel?

VIEW SOLUTION

Exercise 14.1 | Q 7 | Page 28

50 circular plates each of diameter 14cm and thickness 0.5cm are placed one above other to form a right circular cylinder. Find its total surface area?

VIEW SOLUTION

Exercise 14.1 | Q 8 | Page 28

25 circular plates each of radius 10.5cm and thickness 1.6cm are placed one above the other to form a solid circular cylinder. Find the curved surface area and volume of cylinder so formed?

VIEW SOLUTION

Exercise 14.1 | Q 9 | Page 28

Find the number of metallic circular discs with 1.5 cm base diameter and of height 0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm .

VIEW SOLUTION

Exercise 14.1 | Q 10 | Page 28

How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimension 6cm

× 42cm × 21 cm. VIEW SOLUTION

Exercise 14.1 | Q 11 | Page 28

How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm .

VIEW SOLUTION

Exercise 14.1 | Q 12 | Page 28

Three cubes of a metal whose edges are in the ratios 3 : 4 : 5 are melted and converted into a single cube whose diagonal is

123

. Find the edges of the three cubes.

VIEW SOLUTION

Exercise 14.1 | Q 13 | Page 28

A solid metallic sphere of radius 10.5 cm is melted and recast into a number of smaller cones, each of radius 3.5 cm and height 3 cm. Find the number of cones so formed.

VIEW SOLUTION

Exercise 14.1 | Q 14 | Page 28

The diameter of a metallic sphere is equal to 9cm. it is melted and drawn into a long wire of diameter 2mm having uniform cross-section. Find the length of the wire?

VIEW SOLUTION

Exercise 14.1 | Q 15 | Page 28

An iron spherical ball has been melted and recast into smaller balls of equal size. If the radius of each of the smaller balls is 1/4 of the radius of the original ball, how many such balls are made? Compare the surface area, of all the smaller balls combined together with that of the original ball.

VIEW SOLUTION

Exercise 14.1 | Q 16 | Page 28

A copper sphere of radius 3cm is melted and recast into a right circular cone of height 3cm.find radius of base of cone?

VIEW SOLUTION

Exercise 14.1 | Q 17 | Page 28

A copper rod of diameter 1cm and length 8cm is drawn into a wire of length 18m of uniform thickness. Find thickness of wire?

VIEW SOLUTION

Exercise 14.1 | Q 18 | Page 28

The diameters of internal and external surfaces of hollow spherical shell are 10cm and 6cm respectively. If it is melted and recast into a solid cylinder of length of 2

23 cm, find the

diameter of the cylinder.

VIEW SOLUTION

Exercise 14.1 | Q 19 | Page 28

How many coins 1.75cm in diameter and 2mm thick must be melted to form a cuboid 11cm x 10cm x 75cm___?

VIEW SOLUTION

Exercise 14.1 | Q 20 | Page 28

The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed (Use it =

227 ) VIEW SOLUTION

Exercise 14.1 | Q 21 | Page 29

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

VIEW SOLUTION

Exercise 14.1 | Q 22 | Page 29

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