## NCERT Class 10 Maths Lab Manual – Volume of a Cone

**Objective**

To get the formula for the volume of a right circular cone experimentally.

**Prerequisite Knowledge**

- Formula for the volume of cylinder.
- Concept of volume and its proportionality to the quantity of matter.

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

**Materials Required**

One cone and one cylinder having the same height and base radius, sand.

**Procedure**

- Fill the cone with sand.
- Pour the sand from the cone to the cylinder.
- Fill the cone with sand again and pour to the cylinder.
- Repeat the same process until the cylinder fills completely with sand.

**Observation and Result**

Students will observe that the cylinder gets filled after pouring the sand three times from cone.

Volume of cone =\( \frac { 1 }{ 3 } \)Volume of cylinder =\(\frac { 1 }{ 3 } \quad \pi { r }^{ 2 }h\)

**Learning Outcome**

Through this experiment, students will learn the relationship between the volume of a cone and a cylinder.

**Activity Time**

- Find volume of cone.
- What will be the volume of the cylinder having same height and radius given above ?

**Viva Voce**

**Question 1:**

Radius of a cone is halved and height is doubled. What effect will be on its volume ?

**Answer:
**It will be half of original

**Question 2:**

Radii of two cones of same heights are in the ratio 2:5. Find the ratio of their volume.

**Answer:**

4:25.

**Question 3:**

What is the volume of a cone ?

**Answer:**

\(\frac {1}{3}\quad \pi{ r }^{ 2 }h\)

**Question 4:**

Can we say that volume of a cone is 3 times the volume of a cylinder ?

**Answer:**

No.

**Question 5:**

Two cones have their heights in the ratio 1 : 3 and the radii of their bases are in the ratio 3:1. What is the ratio of their volumes ?

**Answer:
**3:1.

**Question 6:**.

Base radii of two cones of same heights are in the ratio 3:5. Find the ratio of their volumes ?

**Answer:**

9:25.

**Question 7:**

What is the ratio of the volume of a cylinder to volume of a cone of same height and same base ?

Ans.

3:1.

**Question 8:**

Ratio of volumes of two cones having, the same base radius is 9:25, then what is the ratio of their heights ?

**Answer:**

9:25.

**Multiple Choice Questions**

**Question 1:**

The height of a cone is 15 cm. If its volume is 1571.4 cm^{3}. Then radius of the base is

(a) 10 cm

(b) 15 cm

(c) 5 cm

(d) none of these

**Question 2:**

Volume of the right circular cone with radius 3.5 cm, height 12 cm is

(a) 145 cm^{3
}(b) 154 cm^{3
}(c) 541 cm^{3
}(d) none of these

**Question 3:**

The volume of a largest right circular cone that can be fit in a cube whose edge is 14 cm, is

(a) 71.86 cm^{3
}(b) 781.6 cm^{3
}(c) 718.6 cm^{3
}(d) none of these

**Question 4:**

The radius and height of right circular cone are in the ratio 5 :12. If its volume is 2512 cm^{3 }. Then slant height is

(a) 10 cm

(b) 24 cm

(c) 26 cm

(d) none of these

**Question 5:**

A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m, then volume is

(a) 86.625 m^{3
}(b) 8.6625m^{3}

(c) 866.25 m^{3}

(d) none of these

**Question 6:**

A semi-circular thin sheet of metal of diametet 28 cm is bent to make an open conical cup. Then the capacity of the cup is

(a) 622.36 cm^{3}

(b) 62.236 cm^{3}

(c) 6223.6 cm^{3}

(d) none of these

**Question 7:**

Volume of a cone of base radius 6 cm is 264 cm’. Ther its height is

(a) 5 cm

(b) 6 cm

(c) 7 cm

(d) none of these

**Question 8:**

Volume of a cone of height 12 cm is 154 cm . Then the diameter of the base is

(a) 3.5 cm

(b) 7 cm

(c) 3.4 cm

(d) 7.1 cm

**Question 0:**

The volume of a right circular cone with radius 6 cm and height 7 cm is

(a) 246 cm

(b) 264 cm

(c) 462 cm

(d) none of these

**Question 10:**

The volume of a cone is 1540 cm . If the radius of its base is 10 cm, then the height of the cone is

(a) 147 cm

(b) 14.8 cm

(c) 14.7 cm

(d) 1.47 cm

**Answers**

1. (a)

2. (b)

3. (c)

4. (d)

5. (a)

6. (d)

7. (c)

8. (b)

9. (b)

10. (c)

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