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

**Objective**

To find the surface area of sphere with the help of an activity.

**Prerequisite Knowledge**

Curved surface area (C.S. A.)of a right circular cylinder = (where r =radius of the base and h = height of the cylinder)

**Materials Required**

A solid spherical plastic ball, a cylinder with height equal to the diameter of the sphere, thread, cutter, pins, sketch pen etc. (Let radius of sphere be rand height of the cylinder be h)

**Procedure**

- Divide the spherical plastic ball into two hemispherical portion with the help of a cutter.
- Fix a pin at the top most point of the hemisphere.
- Take a roll of thread and wind it closely on the curved surface of the hemisphere completely in the form of spiral starting with the pin on the surface of the hemisphere
- Take another roll of thread and wind it completely along the curved surface of the cylinder in the form of a spiral.
- Unwind the threads from the hemisphere and cylinder.
- Compare the length of two threads used in wrapping.

**Observation**

- The length of the thread used to cover the cylinder is two times more than the length of the thread used to cover the hemisphere.
- Curved surface area of the hemisphere = x curved surface area of cylinder

(i.e h=2r because height of the cylinder = diameter of sphere)

Total surface area of sphere =2x

**Result**

Surface area of a sphere = (verified experimentally).

**Learning Outcome**

Students will derive the formula for surface area of a sphere through an activity.

**Activity Time**

Let the radii of a sphere and of the base of a cylinder are same. Find the ratio of the curved surface area of a sphere to curved surface area of a cylinder if the height of the cylinder is 2 times of its radius.

**Viva Voce**

**Question 1:**

What is a hemisphere ?

**Answer:**

Half of a sphere is called a hemisphere.

**Question 2:**

How many hemispheres make a sphere ?

**Answer:**

Two

**Question 3:**

What is the curved surface area of a hemisphere ?

**Answer:**

**Question 4:**

What is the curved surface area of a sphere ?

**Answer:**

**Question 5:**

What is the total surface area of a hemisphere ?

**Answer:**

**Question 6:**

What is the surface area of a sphere of diameter 14 cm ?

**Answer:**

616 cm^{2}

**Question 7:**

What is the radius of a hemisphere whose total surface area is 942 cm ? [Take 71 — 3.14 ]

**Answer:**

10 cm

**Question 8:**

What is the curved surface area of a sphere of radius 3 cm ? ’

**Answer:**

36 cm^{2}

**Multiple Choice Questions**

**Question 1:**

Surface area of a sphere of diameter 21 cm is

(a) 1386 cm^{2}

(b) 1368 cm^{2}

(c) 1683 cm^{2}

(d) 1863 cm^{2}

**Question 2:**

Find the total surface area of a hemisphere of radius 10cm. [Taken = 3.14]

(a) 924 cm^{2}

(b) 492 cm^{2}

(c) 942 cm^{2}

(d) None

**Question 3:**

The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

(a) 4:1

(b) 1:4

(c) 1:1

(d) 4:4

**Question 4:**

What is the radius of a sphere whose surface area is 154 cm” ?

(a) 3.5 cm

(b) 3.3 cm

(c) 5.3 cm

(d) 5.5 cm

**Question 5:**

The diameter of the moon is approximately one- fourth of the diameter of the earth. Find the ratio of their surface areas.

(a) 1:16

(b) 16:1

(c) 1:4

(d) none of these

**Question 6:**

A right circular cylinder just encloses a sphere of radius r. Then what is the ratio of surface area of the sphere to curved surface area of the cylinder ?

(a) 1:1

(b) 4:1

(c) 1:4

(d) none of these

**Question 7:**

A sphere of radius rhas the same volume as that of a cone with a circular base of radius r. Find the height of the cone.

(a) 2 r

(b) 4 r

(c) 3 r

(d) none of these

**Question 8:**

What is the surface area of a sphere of diameter 3.5 m ?

(a) 38.5 m^{2}

(b) 35.8 m^{2}

(c) 53.8 m^{2}

(d) none of these

**Question 9:**

If the radii of a sphere and base of a cylinder are same, then find the ratio of the curved surface area of sphere to curved surface area of the cylinder if height of the cylinder is 4 times of its radius.

(a) 2:1

(b) 1:2

(c) 1:4

(d) 4:1

**Question 10:**

If the surface area of a sphere is 5544 cm^{2}, then its diameter is

(a) 42 cm

(b) 24 cm

(c) 22 cm

(d) 44 cm

**Answers**

1. (a)

2. (c)

3. (b)

4. (a)

5. (a)

6. (a)

7. (b)

8. (a)

9. (b)

10.(b)

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