# NCERT Solutions for Exercise 13.3 Class 9 Maths Chapter 13 - Surface Area and Volumes

NCERT Solutions for Class 9 Maths exercise 13.3 deals with the concept of the right circular cone and it’s surface areas . A three-dimensional shape which narrows smoothly from a flat base to a point is known as cone. Mathematically, there are two types of cones namely right circular cone and oblique cone. In exercise 13.3 Class 9 Maths, a type of cone whose axis falls perpendicular on the plane of the base is known as the right circular cone. The distance from the vertex or apex to the point on the outer line of the circular base of the cone is known as slant height which is derived from the Pythagoras Theorem. The formula for calculating the slant height of right circular cone is l^{2}=r^{2}+h^{2}, from the formula l can be calculated. The surface area of a right circular cone is the area covered by the surface of the right circular cone. Surface area can be divided into two categories. They are

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Area of Lateral Surface

Area of Total Surface

The curved surface area of the right circular cone, also known as the lateral surface area of the right circular cone, is the area covered by the curved surface of the cone. The total surface area of the right circular cone is the area occupied by the complete cone . NCERT solutions for Class 9 Maths chapter 13 exercise 13.3 include eight questions, seven of which are simple and the remaining one may take some time to complete . This Class 9 Maths chapter 13 exercise 13.3 thoroughly explains the concepts of surface area and volume. Along with Class 9 Maths chapter 13 exercise 13.3 the following exercises are also present.

- Surface Area and Volumes Exercise 13.1
- Surface Area and Volumes Exercise 13.2
- Surface Area and Volumes Exercise 13.4
- Surface Area and Volumes Exercise 13.5
- Surface Area and Volumes Exercise 13.6
- Surface Area and Volumes Exercise 13.7
- Surface Area and Volumes Exercise 13.8
- Surface Area and Volumes Exercise 13.9

** ****Surface Area and Volumes C**lass 9 Chapter 13 Exercise: 13.3

**Surface Area and Volumes C**lass 9 Chapter 13 Exercise: 13.3

** Q1 ** Diameter of the base of a cone is and its slant height is . Find its curved surface area.

** Answer: **

Given,

Base diameter of the cone =

Slant height =

We know, Curved surface area of a cone

Required curved surface area of the cone=

** Q2 ** Find the total surface area of a cone, if its slant height is and diameter of its base is .

** Answer: **

Given,

Base diameter of the cone =

Slant height =

We know, Total surface area of a cone = Curved surface area + Base area

Required total surface area of the cone=

** Q3 (i) ** Curved surface area of a cone is and its slant height is 14 cm. Find radius of the base .

** Answer: **

Given,

The curved surface area of a cone =

Slant height

(i) Let the radius of cone be

We know, the curved surface area of a cone=

Therefore, the radius of the cone is

** Q3 (ii) ** Curved surface area of a cone is and its slant height is . Find total surface area of the cone.

** Answer: **

Given,

The curved surface area of a cone =

Slant height

The radius of the cone is

(ii) We know, Total surface area of a cone = Curved surface area + Base area

Therefore, the total surface area of the cone is

** Q4 (i) ** A conical tent is 10 m high and the radius of its base is 24 m. Find slant height of the tent.

** Answer: **

Given,

Base radius of the conical tent =

Height of the conical tent =

Slant height =

Therefore, the slant height of the conical tent is

** Q4 (ii) ** A conical tent is 10 m high and the radius of its base is 24 m. Find cost of the canvas required to make the tent, if the cost of canvas is Rs 70.

** Answer: **

Given,

Base radius of the conical tent =

Height of the conical tent =

Slant height =

We know, Curved surface area of a cone

Curved surface area of the tent

Cost of of canvas =

Cost of of canvas =

Therefore, required cost of canvas to make tent is

** Q5 ** What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm (Use ).

** Answer: **

Given,

Base radius of the conical tent =

Height of the tent =

We know,

Curved surface area of a cone =

Area of tarpaulin required = Curved surface area of the tent

Now, let the length of the tarpaulin sheet be

Since is wasted, effective length =

Breadth of tarpaulin =

Therefore, the length of the required tarpaulin sheet will be 63 m.

** Q6 ** The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of Rs 210 per .

** Answer: **

Given, a conical tomb

The base diameter of the cone =

Slant height

We know, Curved surface area of a cone

Now, Cost of whitewashing per =

Cost of whitewashing per =

Therefore, the cost of white-washing its curved surface of the tomb is .

** Q7 ** A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.

** Answer: **

Given, a right circular cone cap (which means no base)

Base radius of the cone =

Height

We know, Curved surface area of a right circular cone

The curved surface area of a cap =

The curved surface area of 10 caps =

Therefore, the area of the sheet required for 10 caps =

** Q8 ** A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs 12 per , what will be the cost of painting all these cones? (Use and take )

** Answer: **

Given, hollow cone.

The base diameter of the cone =

Height of the cone =

Slant height =

We know, Curved surface area of a cone =

The curved surface area of 1 cone =

The curved surface area of 50 cones

Now, the cost of painting area =

Cost of the painting area

Therefore, the cost of painting 50 such hollow cones is

**More About NCERT Solutions for Class 9 Maths Exercise 13.3: Surface Area and Volumes – right circular cone **

The NCERT solutions for Class 9 Maths exercise 13.3 is mainly focused on the surface area of the right circular cone. In exercise 13.4 Class 9 Maths, The curved surface area of a cone can be calculated by multiplying the area of the sector with radius length . The area of the lateral surface plus the area of the circular base equals the total surface area of a closed right circular cone. V=πr^{2}×h/3 is the volume of a right circular cone, which is one-third of the product of the circular base's area and its height. Surface areas are measured in square units, but the volume of a cube is measured in cubic units. In NCERT solutions for Class 9 Maths exercise 13.3, the formulas for computing surface areas and volume for the correct circular cone are thoroughly explored.

**Also Read| **Surface Areas And Volumes Class 9 Notes

**Benefits of NCERT Solutions for Class 9 Maths Exercise 13.3 : **

• NCERT solutions for Class 9 Maths exercise 13.3 will help us to easily identify the object which resembles the cone shape example: an ice cream cone.

•NCERT book Exercise 13.3 Class 9 Maths, clearly explained the formula for calculating the curved surface area of the right circular cone step by step for our better understanding.

• By completing the NCERT syllabus Class 9 Maths chapter 13 exercise 13.3 exercises, we can build a solid foundation of mathematical knowledge as well as gain confidence in approaching new topics in our higher classes.

**Also See:**

NCERT Solutions for Class 9 Maths Chapter 13 – Surface Area and Volumes

NCERT Example Solutions Class 9 Maths Chapter 13 – Surface Area and Volumes

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