Let the internal and external radii of a hollow cylinder be r and R units respectively. If the height of the cylinder is h units then

**Volume of a hollow cylinder (volume of the
material used)**

Let the internal and external radii of a hollow cylinder be *r*
and *R* units respectively. If the height of the cylinder is *h*
units then

V = *πR *^{2}*h* − *πr*^{2}*h*
= *π(R* ^{2} −*r*^{2} )*h*

Volume of a hollow cylinder = *π(R* ^{2} −*r*^{2}
)*h* cu. units.

**Example 7.15**

Find the volume of a cylinder whose height is** **2** **m and whose base area** **is 250 m^{2}.

*Solution*

Let* **r*** **and

Given that, height *h* = 2 m, base area = 250 m^{2}

Now, volume of a cylinder = *πr*^{2}*h* cu.
Units

*= base area *×* h*

= 250×2 = 500 m^{3}

Therefore, volume of the cylinder = 500 m^{3}

**Example 7.16**

The volume of a cylindrical water tank is** **1.078** **×** **10^{6}** **litres. If the diameter** **of the tank is 7 m, find
its height.

*Solution*

Let* **r*** **and

Given that, volume of the tank = 1.078 ×10^{6} = 1078000
litre

= 1078 m^{3}

= 1078 m^{3} (since 1*l* =
1/1000 m^{3})

diameter = 7m gives radius = 7/2 m

volume of the tank = *πr ^{2}h*
cu. Units

1078 = 22/7 × 7/2 × 7/2 ×*h*

Therefore, height of the tank is 28 m

**Example 7.17**

Find the volume of the iron used to make a hollow cylinder of
height**
**9** **cm** **and whose internal and
external radii are 21 cm and 28 cm respectively.

** Solution **Let

Given that, *r* =21cm, *R* = 28 cm, *h* = 9 cm

Now, volume of hollow cylinder = *π(R*^{2} −*r*^{2}
)*h* cu. Units

= 22/7 (28^{2} − 21^{2} )×9

= 22/7 (784 − 441) ×9 = 9702

Therefore, volume of iron used = 9702 cm^{3}

**Example 7.18**

For the cylinders** ***A*** **and** ***B*** **(Fig. 7.27),

(i) find out the cylinder whose volume is greater.

(ii) verify whether the cylinder with greater volume has greater
total surface area.

(iii) find the ratios of the volumes of the cylinders *A* and
*B*.

*Solution*

(i) Volume of cylinder = *πr*^{2}*h* cu. Units

Volume of cylinder *A* = 22/7 × 7/2 × 7/2 ×21

= 808. 5 cm^{3}

Volume of cylinder *B *= 22/7 × 21/2 × 21/2 × 7

= 2425. 5 cm^{3}

Therefore, volume of cylinder *B* is greater than volume of
cylinder *A*.

(ii) T.S.A. of cylinder = 2*πr *(*h* + *r*) sq.
units

T.S.A. of cylinder *A* = 2 × (22/7) × (7/2) ×(21 + 3. 5) =
539 cm^{2}

T.S.A. of cylinder *B* = 2 × (22/7) × (21/2) ×(7 + 10. 5) =
1155 cm^{2}

Hence verified that cylinder *B* with greater volume has a
greater surface area.

(iii)

Therefore, ratio of the volumes of cylinders *A* and *B*
is 1:3.

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