RD Chapter 19- Surface Areas and Volume of a Circular Cylinder Ex-19.1 |
RD Chapter 19- Surface Areas and Volume of a Circular Cylinder Ex-VSAQS |

A soft drink is available in two packs – (i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and

(ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much? [NCERT]

**Answer
1** :
In first case, in a rectangular container of softdrink, the length of base = 5 cm

and Width = 4 cm

Height = 15 cm

∴ Volume of soft drink = lbh= 5 x 4 x 15 = 300 cm^{3}

and in second case, in a cylindrical container, diameter of base = 7 cm

Thesoft drink in second container is greater and how much greater = 385 cm – 380cm^{2} = 85 cm^{2}

**Answer
2** :
Radius of each pillar (r) = 20 cm

**Answer
3** :
Inner diameter of a cylindrical wooden pipe = 24 cm

(i) radius of its base

(ii) volume of the cylinder [Use π = 3.14] [NCERT]

**Answer
4** :
Lateral surface area of a cylinder = 94.2 cm2

**Answer
5** :
The capacity of a closed cylindrical vessel = 15.4 l

**Answer
6** :
Diameter of the cylindrical bowl = 7 cm

∴ Radius (r) = 7/2cm

Level of soup in it = 4 cm

∴ Volume of soup in one bowlfor one patient

**Answer
7** :
Width of hollow cylinder (A) = 63 cm

Girth = 440 cm

**Answer
8** :
Rate of painting = 50 paise per dm^{2}

Total cost = ₹198

**Answer
9** :

Ratio in radii of two cylinders = 2:3

and ratio in their heights = 5:3

Let radius of the first cylinder (r_{1}) = 2x

and radius of second cylinder (r_{2}) = 3x

and height of first cylinders (h_{1}) = 5y

and height of second cylinder (h_{2}) = 3y

(i) Now volume of the first cylinder = πr^{2}h = π(2x)^{2} x5y = 20πx^{2}2y

and volume of tlie second cylinder = π(3x)^{2} x 3y = π x 9×2 x 3y= 27πx^{2}y

Now ratio in their volume

= 20πx^{2}y : 21πx^{2}y = 20 : 27

(ii) Curved surface area of first cylinder = 2πrh = 2π x 2x x 5y =20πxy

and curved surface area of second cylinder = 2π x 3x x = 1 8πxy

∴ Ratioin their curved surface area

= 20πxy : 18πxy = 10 : 9

**Answer
10** :
Ratio in curved surface area and total surface area ofa cylinder =1:2

Total surface area = 616 cm^{2}

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