Page 15.62

### EXERCISE 15.3

**Type 1**

#### QUESTION 1

**Fill in the blanks :**

**In a right circular cone :**

**(i) h=4 m and r=3 m , l= __**

**(ii) l=10 cm and r=7 cm , curved surface area A = _**

**(iii) r=7 m and h=9m , volume V=__**

**(iv) l=25 cm and r=7 m , height h=__**

**(v) l=13 cm and h=12 cm , radius r =__**

#### QUESTION 2

**Total surface area of a right circular cone is obtained by S =__**

Sol :

#### QUESTION 3

**If base and height of a right circular cone and a right circular cylinder be the same :**

**Which of the following will be the relation between their volumes ?**

**(a) Volume of the cone < Volume of the cylinder**

**(b) Volume of the cone > Volume of the cylinder**

**(c) Volume of the cone = Volume of the cylinder**

**(d) none of these**

Sol :

#### QUESTION 4

**Ratio of the volumes of a right circular cylinder and right circular cone is :**

**(a) 1:3**

**(b) 3:1**

**(c) 4:3**

**(d) 3:3**

Sol :

#### QUESTION 5

**Which of the following will be the relation between the volume of a cube with edge a cm and a cone having base radius a cm and height a cm :**

**(a) 3:π**

**(b) π:3**

**(c) 1:3**

**(d) 3:1**

Sol :

#### QUESTION 6

**Two cones have the same height and ratio of the radii as 1:2 . Which of the following will be the ratio between their volumes ?**

**(a) 2:1**

**(b) 1:2**

**(c) 1:4**

**(d) 4:1**

Sol :

#### QUESTION 7

**If radius and height, both of a right circular cone be doubled, which of the following will be the ratio between the volumes of new solid and original solid?**

**(a) 2:1**

**(b) 1:2**

**(c) 6:1**

**(d) 8:1**

Sol :

#### QUESTION 8

**If base radius of right circular cone be halved , keeping the height unchanged which of the following will be the ratio between the volumes of original cone and the miniature cone ?**

**(a) 1:2**

**(b) 2:1**

**(c) 1:4**

**(d) 4:1**

Sol :

#### QUESTION 9

**The height of a right circular cone is and its base radius is . What will be the volume of the cone ?**

**(a)**

**(b)**

**(c)**

**(d)**

Sol :

#### QUESTION 10

**The radius of the base of a cone is 3cm and height is 7cm , then find its volume .**

Sol :

#### QUESTION 11

**The radius of the base of a cone is 3cm and height is 4cm , find its volume **

Sol :

#### QUESTION 12

**The diameter of the base of a conical canvas tent is 14m and its slant height is 6m , find the area of the canvas used in the tent .**

Sol :

#### QUESTION 13

**Diameters of two cones are same . If their slant heights are in the ratio 5:4 , find the ratio of their curved surfaces**

Sol :

#### QUESTION 14

**There are two cones. The curved surface area of one is twice the curved surface area of the other . The slant height of the second is twice that of the first . Find ratio of their radii**

Sol :

#### QUESTION 15

**Find the curved surface area of a right circular cone whose slant height is 10cm and base radius is 7cm**

Sol :

#### QUESTION 16

**The height of a cone is 16cm and radius of the base is 12cm . Find the curved surface area of this cone . (Use π=3.14)**

Sol :

#### QUESTION 17

**The radius of the base of a cone is 7cm and its height is 24cm . Find its total surface area.**

Sol :

#### QUESTION 18

**The circumference of the base of a 10m high conical tent is 44m . One another conical tent has 20m and circumference 22m . What will be the ratio of the volume of the first and the second tent ?**

**(a) 8:1**

**(b) 2:1**

**(c) 1:8**

**(d) 1:4**

Sol :

#### QUESTION 19

**Radius of the base of a cone and height are respectively 35cm and 72cm . Find the**

**(i) volume**

**(ii) curved surface area **

**(iii) total surface area of the cone **

Sol :

#### QUESTION 20

**A conical cup is formed by bending a semicircular metal sheet of diameter 28cm . Find the capacity of the cup.**

Sol :

#### QUESTION 21

**Curved surface area of a cone is 4970 cm ^{2} and its diameter is 70cm . Find its slant height **

Sol :

#### QUESTION 22

**The slant height of a cone is 7 m and its curved surface area is 440 m ^{2 }. Find the radius of its base .**

Sol :

#### QUESTION 23

**The curved surface area of a right circular cone with radius 11.3 cm is 355 cm ^{2}. What is the slant height of the cone ? **

Sol :

#### QUESTION 24

**Total surface area of a cone is 22 m ^{2 }. Its slant height is 6 times the radius of the base **

Sol :

#### QUESTION 25

**The volume of a cone is 770 m ^{3 }and its height is 15m . Find the radius of the base **

Sol :

#### QUESTION 26

**(i) A right triangle with sides 7cm and 12cm forming a right angle is revolved about the 12cm side . Find the volume of the cone so obtained.**

**(ii) Find the volume of the greatest right circular cone which can be made out of cutting a cube whose each edge is 28cm**

Sol :

#### QUESTION 27

**First persons live in a conical tent and for each person , 16m ^{2 }space on the base and 100m^{3} air is required . Find the height of the tent **

Sol :

**PAGE 15.65**

#### QUESTION 28

**A rent of a Circus is cylindrical to a height of 4m and then after height , it is conical above . If its diameter is 112m and slant height of the cone is 75m, find the required total area of the canvas**

Sol :

#### QUESTION 29

**A conical hole of height 8cm and base radius 6 cm is cut out from a solid cylinder of height 8cm and base radius 6cm . Find the volume of the remaining solid.**

Sol :

#### QUESTION 30

**A tent in the shape of a cone is to be made of canvas. Its diameter of the base is 16m and height is 15m . If width of the canvas is 2.2m , what length in metres of canvas will be required ?**

Sol :

**TYPE 2**

#### QUESTION 31

**(i) Find the curved surface area of a right circular cone of height 12 cm with diameter of base as 10cm**

**(ii) If height of a cone is 84cm and base radius is 35cm , find the surface area and volume of the cone**

Sol :

#### QUESTION 32

**The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface .**

Sol :

#### QUESTION 33

**The radius of the base of a right circular cone is 10 cm and its slant height is 15cm . Find the volume and total surface area of the cone.**

Sol :

#### QUESTION 34

**If area of the curved surface of the cone is 396 m ^{2 }and area of its base is 36π m^{2 }, find the slant height of the cone**

Sol :

#### QUESTION 35

**How many opened bags of wheat can be accommodated in a conical tent having radius 8.4m and vertical height 2.5m , if a bag of wheat requires 1.96m ^{3 }of space (π=3.14)**

Sol :

#### QUESTION 36

**A heap of wheat is in the form of a cone whose diameter is 9m and height is 3.5m . Find its volume . How much canvas cloth will be required to cover the heap properly ?**

Sol :

#### QUESTION 37

**A right triangle with sides 3cm and 4cm forming a right angle is revolved about its hypotenuse . Find the volume of the solid so obtained .**

Sol :

#### QUESTION 38

**A right triangle with sides 5cm and 12cm forming a right angle is revolved about its hypotenuse . Find the volume of the solid so obtained.**

Sol :