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KC Sinha Mathematics Solution Class 9 Chapter 15 Surface Areas and Volume exercise 15.3

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 \dfrac{1}{2}x and its base radius is \dfrac{4}{5}x . What will be the volume of the cone ?

(a) \dfrac{32}{75}\pi x^3

(b) \dfrac{8}{25}\pi x^3

(c) \dfrac{8}{75}\pi x^3

(d) \dfrac{2}{25}\pi x^3

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 \left(\pi =\dfrac{22}7{}\right)

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 cm2 and its diameter is 70cm . Find its slant height \left(\pi =\dfrac{22}{7}\right)

Sol :

 


QUESTION 22

The slant height of a cone is 7 m and its curved surface area is 440 m2 . 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 cm2. What is the slant height of the cone ? \left(\pi=\dfrac{355}{113}\right)

Sol :

 


QUESTION 24

Total surface area of a cone is 22 m2 . Its slant height is 6 times the radius of the base 

Sol :

 


QUESTION 25

The volume of a cone is 770 m3 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 , 16m2 space on the base and 100m3 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 m2 and area of its base is 36π m2 , 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 1.96m3 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 :

 


 

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