**NCERT Class 10 Maths Lab Manual – Volume of a Sphere**

**Objective**

To find the formula for the volume of a sphere with the help of an activity.

**Prerequisite Knowledge**

Volume of a cylinder = πr^{2}h

**Materials Required**

A hollow hemispherical plastic ball, a cylinder with diameter and height both equal to the diameter of hemisphere, sand.

**Procedure**

- Take a hollow hemisphere and fill it with sand and empty it into the cylinder.fig, (i).

- Again fill the hemisphere with sand and empty it into the same cylinder second time. fig. (ii).

- Again fill the hemisphere with sand and empty it into the same cylinder third time., fig. (iii).

**Observation**

We observe that the cylinder is completely filled up by pouring sand three times through hemispherical ball.

∴3 x Volume of hemisphere = Volume of cylinder with radius r and height 2r

∴3 x Volume of hemisphere = πr^{2}(2r) = 2πr^{3}

∴Volume of a hemisphere = \(\frac{2\pi{r}^{3}}{3}\)

∴ Volume of sphere = 2 x \(\frac { 2\pi { r }^{ 3 } }{ 3 }\) = \(\frac{4\pi{r}^{3}}{3}\)

**Result**

Volume of a sphere = \(\frac{4\pi{r}^{3}}{3}\) (verified experimentally).

**Learning Outcome**

Smdents arrive at the formula for the volume of a sphere and they are able to relate it with the volume of a cylinder.

Volume of a sphere = volume of a cylinder.

⇒ \(\frac{4\pi{r}^{3}}{3}\) = πr^{2}h (if they have same radius and volume)

∴h = \(\frac { 4 }{ 3 }\) r

**Activity Time**

If the radius of the sphere is tripled, then what will be the effect on its volume ? Verify it by an activity.

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

**Viva Voce**

**Question 1.**

What is the formula for volume of a hemisphere ?

**Answer:**

\(\frac{2\pi{r}^{3}}{3}\) , where r = radius of hemisphere

**Question 2.**

If the number of square centimetres on the surface of a sphere is equal to the number of cubic centimetres in its volume. What is the radius of the sphere ?

**Answer:**

3 cm

**Question 3.**

What is the volume of a sphere ?

**Answer:**

\(\frac{4\pi{r}^{3}}{3}\) , where r is the radius of the sphere

**Question 4.**

How many balls each of radius 1 cm can be made from a solid sphere of lead of radius 8 cm ?

**Answer:**

512 balls

**Question 5.**

Metallic spheres of radii 3 cm, 4 cm and 5 cm respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.

**Answer:**

6 cm

**Question 6.**

What is the ratio of the volume of a cube to that of a sphere which will exacdy fit inside the cube ?

**Answer:**

6 : π

**Question 7.**

What is the ratio of the volume of a sphere to that of a cone whose height and radius of base are same as radius of the sphere ?

**Answer:**

4:1

**Question 8.**

What is the ratio of the volume of a hemisphere to that of a sphere of same radius?

**Answer:**

1:2

**Multiple Choice Questions**

**Question 1.**

What is the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube ?

(a) 6 : π

(b) π : 6

(c) π : 3

(d) 3 : π

**Question 2.**

The largest sphere is carved out of a cube of side 7 cm. The volume of the sphere is

(a) 179.5 cm^{3}

(b) 197.5 cm^{3}

(c) 791.5 cm^{3}

(d) 971.5 cm^{3}

**Question 3.**

If the surface area of a sphere is 616 cm^{3}, then its volume is

(a) 1473.3 cm^{3}

(b) 1437.3 cm^{3}

(c) 1743.3 cm^{3}

(d) none of these

**Question 4.**

How many litres of milk can a hemispherical bowl of a diameter 10.5 cm hold ?

(a) 0.309 l

(b) 0.330 l

(c) 0.303 l

(d) 0.003 l

**Question 5.**

Find the volume of a sphere of radius 0.63 m.

(a) 1.05 m^{3}

(b) 2.05 m^{3}

(c) 3.05 m^{3}

(d) none of these

**Question 6.**

How many lead balls each of 3 cm radius can be made from a sphere of radius 12 cm ?

(a) 62

(b) 64

(c) 63

(d) 61

**Question 7.**

A hemispherical bowl has a radius of 3.5 cm. What would be the volume of water it would contain ?

(a) 64 cm^{3}

(b) 63 cm^{3}

(c) 62 cm^{3}

(d) none of these

**Question 8.**

A metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones each of diameter 7 cm and height 3 cm. Find the number of cones so formed.

(a) 162

(b) 126

(c) 612

(d) 621

**Question 9.**

The diameter of a sphere is 42 cm. It is melted and drawn into a cylindrical wire of diameter 28 cm. Find the length of the wire.

(a) 63 cm

(b) 61cm

(c) 64 cm

(d) 60 cm

**Question 10.**

The diameter of the moon is approximately one-fourth the diameter of the earth. What fraction of the volume of the earth is the volume of the moon ?

(a) 1 : 64

(b) 64 : 1

(c) 1 : 1

(d) none of these

**Answers**

1. (a)

2. (a)

3. (b)

4. (c)

5. (a)

6. (a)

7. (d)

8. (a)

9. (a)

10. (a)

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