## NCERT Class 10 Maths Lab Manual – Surface Area of a Cone

**Objective**

To find the formula for the lateral surface area and total surface area of a right circular cone experimentally.

**Prerequisite Knowledge**

- Area of circle =\({\pi }{r}^{2}\)
- Area of parallelogram = b x h (b =base, h = height).
- Circumference of circle = \(2{\pi }{r}\)

You can also download **NCERT Solution Of Maths Class 10** to help you to revise complete syllabus and score more marks in your examinations.

**Materials Required**

A cone made of chart paper, a pair of scissors, geometry box, fevicol, cello tape.

**Procedure**

- Make a cone of pink chart paper having base radius r, slant height ‘l’ and height h.
- Cut the cone along slant height as shown in fig (i) as per dotted line and unroll it to get a sector, as shown in fig. (ii). Name this sector OAB.
- Identify the arc length AB of the sector OAB = circumference of the base of the cone. radius of the sector OAB = slant height of the cone. As shown in the fig. (ii).
- Cut the sector OAB into 4 small equal sectors, along dotted lines as shown in fig. (ii) and fill red colour in two sectors as shown.
- Arrange these small sectors to get a parallelogram as shown in fig. (iii).

**Observation**

- Base of parallelogram =\(\frac {1}{2}\)x length of sector OAB =

\(\frac {1}{2}\)×\(2{\pi}{r}\) =\({\pi}{r}\) - Altitude of parallelogram = slant height of cone = l
- Area of parallelogram =\(2{\pi }{r}\) x l= Curved surface area of cone.
- Total surface area of cone =\(2{\pi}{r}l\) + area of circular base of cone.

=\(2{\pi}{r}l\) + \({\pi}{ r}^{2}\)

= \({\pi}{r}\)(l+r)

**Learning Outcome**

Students will learn the concept to differentiate between the curved surface area and total surface area of a cone.

**Activity Time**

- Find lateral surface area of a cone in figure given.
- Find total surface area of a cone in figure given.

**Viva Voce
**

**Question 1:**

What is the relation between slant height and base radius of a cone ?

**Answer:**

\({ l }^{ 2 }={ h }^{ 2 }+{ r }^{ 2 }\) , l= slant height, r— radius of cone, h = height of cone.

**Question 2:**

What is the lateral surface area of a cone ?

**Answer:**

\(\pi rl\) . l= slant height, r— radius of base.

**Question 3:**

What is the total surface area of a cone ?

**Answer:**

\pi r(l+r) . l= slant height, r= radius of base.

**Question 4:**

How many circular faces are there in a solid cone ?

**Answer:**

One.

**Question 5:**

Number of vertex of a cone is

**Answer:**

One.

**Question 6:**

Find slant height of a cone of base radius 3 cm and height 4 cm.

**Answer:**

5 cm.

**Question 7:**

What is the lateral surface area of a cone if its height is 2 times of the radius ?

**Answer:
**\(\sqrt { 5 } \pi { r }^{ 2 }\)

**Question 8:**

What is the radius of the base of a cone of height 6 cm and slant height 10 cm ?

**Answer:
**8 cm.

**Multiple Choice Questions**

**Question 1:**

Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Its curved surface area is

(a) 163 cm^{2
}(b) 165 cm^{2
}(c) 156 cm^{2
}(d) none of these

**Question 2:**

Curved surface area of a cone is 308 cm^{2 }and its slant height is 14 cm. Radius of the base is

(a) 7 cm

(b) 14 cm

(c) 22 cm

(d) none of these

**Question 3:**

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.

(a) 5500 cm^{2
}(b) 5050 cm^{2
}(c) 5005 cm^{2
}(d) none of these

**Question 4:**

The height of a cone is 16 cm and its base radius is 12 cm. Find its curved surface area.

(a) 753.16 cm^{2
}(b) 753.6 cm^{2
}(c) 753.61 cm^{2
}(d) none of these

**Question 5:**

The radius and height of a cone are in the ratio 4 : 3. The area of the base is 154 cm^{2 }. What is the area of its curved surface ?

(a) 129.5 cm^{2 }

(b)195.2 cm^{2 }

(c)192.5 cm^{2}

(d) none of these

**Question 6:**

The radius and slant height of a cone are in the ratio 4:7. If its curved surface area is 792 cm^{2}. Find its radius.

(a) 12 cm

(b) 11cm

(c) 13 cm

(d) 10 cm

**Question 7:**

Curved surface area of a cone of base radius 7 cm is 308 cm^{2}, then its slant height is

(a) 7 cm

(b) 14 cm

(c) 21 cm

(d) 28 cm

**Question 8:**

Total surface area of a cone of base radius 7 cm is 462 cm^{2} , then its slant height is

(a) 14 cm

(b) 28 cm

(c) 12 cm

(d) none of these

**Question 9:**

A conical tent is 10 m high and the radius of its base is 24 m, then its slant height

(a) 24 m

(b) 25 m

(c) 26 m

(d) none of these

**Question 10:**

Curved surface area of a cone of base radius 7 m and slant height 25 m is

(a) 550 m^{2
}(b) 505 m^{2
}(c) 555 m^{2
}(d) none of these

**Answers**

1. (b)

2. (a)

3. (a)

4. (b)

5. (c)

6. (a)

7. (b)

8. (a)

9. (c)

10. (a)

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