Page 15.83

### EXERCISE 15.4

**Type 1**

#### QUESTION 1

**Fill in the Blanks :**

**(i) Volume of a sphere V is __ , where the radius of the sphere is r**

**(ii) Volume of a sphere V is __ , where the diameter of the sphere is r**

**(iii) If a and b the external and internal radii respectively of a spherical shell then its volume V=__**

**(iv) External and internal diameters of a hollow sphere are x and y respectively, then the volume of the solid part of the hollow sphere **

**(v) Surface area of a sphere will be __ cm ^{2}, if its radius is 7 cm.**

#### QUESTION 2

**The diameter of a hemispherical bowl is 12cm , find the internal surface area and capacity [Take π=3.14]**

Sol :

#### QUESTION 3

**A solid is in a circular cylindrical shape , with a hemisphere adjoined on either ends . If total length of this solid is 108 cm and diameter of hemispherical ends is 36 cm , find the cost of colouring at the rate of 7 paise per cm ^{2 }[use π=3.14]**

Sol :

#### QUESTION 4

**A spherical stone has diameter 42 cm and density of stone is 2 gm per cm ^{3}. If any person can lift a weight of 100 kg , then can he lift this stone ? [use π=22/7]**

<hint>

Sol :

**TYPE 2**

#### QUESTION 5

**What is the ratio between the total surface area of a hemisphere and a sphere, when radii of both are equal ?**

Sol :

#### QUESTION 6

**If radius of a sphere be doubled, how many times will its volume increase ?**

Sol :

#### QUESTION 7

**Internal radius of a hemispherical bowl is 6 cm, find its internal surface area.[use π=3.14]**

Sol :

#### QUESTION 8

**Internal diameter of hemispherical bowl is 21cm , find the capacity (volume) of the bowl. [Use π=22/7]**

Sol :

#### QUESTION 9

**A spherical shot putt made of brass has diameter 14 cm. Find its (shot-putt)**

**(i) surface area, (ii) volume.**

Sol :

#### QUESTION 10

**Find the volume and surface area of a sphere of radius 4.3 cm.**

Sol :

#### QUESTION 11

**The volume of a solid hemisphere is , then find its radius.**

Sol :

#### QUESTION 12

**Find the volume and surface area of a sphere having 21 cm radius.**

Sol :

#### QUESTION 13

**The diameter of a metallic ball is 4.2 cm. If the density of its metal is 8.9 gm per cm ^{3} , find the mass of the ball**

Sol :

#### QUESTION 14

**If volume of a sphere is , find its surface area.**

Sol :

#### QUESTION 15

**Curved surface area of a sphere is 616 cm ^{2 } , find the diameter and volume of the sphere**

Sol :

#### QUESTION 16

**Diameter of the moon is approximately one fourth the diameter of the earth. What fraction of the volume of the earth is the volume of the moon ?**

Sol :

#### QUESTION 17

**A toy is in the shape of a right circular cone mounted on a hemisphere . The radius of the base of the cone is 3cm and its height is 4cm . Find the curved surface area and volume of the toy [use π=22/7]**

<fig>

<hint>

Sol :

**TYPE 3**

#### QUESTION 18

**Three solid brass spheres whose radii are 3 cm, 4 cm and 5 cm respectively are melted into a single new sphere . Find the radius of the new sphere.**

Sol :

#### QUESTION 19

**In how many small spheres of 1 cm radius, a sphere of 10 cm radius can be divided ?**

Sol :

#### QUESTION 20

**How many spherical balls of 1cm radius can be casted from a sphere of radius 8cm ?**

Sol :

#### QUESTION 21

**How many spheres of 2 cm diameter can be casted from a cubical piece of lead of side (edge) 22cm ?**

Sol :

#### QUESTION 22

**A sphere of 3 cm radius is melted to stretched into a wire of 0.2 cm diameter. Find the length of the wire.**

Sol :

#### QUESTION 23

**A hemispherical bowl of radius 3 cm is filled with water which is poured into a cylinder of internal radius equal to that of bowl . Find the height of water in the cylinder .**

<hint>

Sol :

#### QUESTION 24

**A metallic cone is 16.8 cm in height and has a base radius of 4.2 cm . If this is melted and casted into a sphere, then find the radius of the sphere.**

Sol :

#### QUESTION 25

**A solid metal sphere of radius 10.5 cm is melted to cast in small cones whose radius is 3.5cm and height is 3cm . Find how many such cones can be made.**

Sol :

#### QUESTION 26

**A com and a hemisphere have same base and equal volumes. Find the ratio of their heights.**

Sol :

#### QUESTION 27

**An iron bar is in the shape of a right circular cylinder with radius 8cm . It is melted and cast into 6 solid spherical balls , the radii of which is equal to the radius of the cylinder . Find the length of the bar.**

Sol :

#### QUESTION 28

**A solid sphere of lead is melted and small shots are casted whose radius is half of the radius of sphere. How many small shots will be casted ? Also , find the ratio of the total surface area of shots and the surface area of the sphere .**

Sol :

#### QUESTION 29

**Oil is contained in a cylindrical jar of radius 6 cm . Iron balls of radius 1.5 cm are dropped in the oil . Find how many balls will be required to be dropped to raise the level of the oil by 2cm .**

<hint>

Sol :

#### QUESTION 30

**A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other . The height and radius of the cylindrical part are 14 cm and 6 cm respectively . The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the surface area of the toy if height of the conical part is 10 cm.**

<fig>

<hint>

Sol :

#### QUESTION 31

**A storage tank consist of a circular cylinder with a hemisphere adjoined on either ends . If the external diameter of the cylinder is 1.0 m and its length is 7 m . What will be the cost of painting the outside at Rs 10 per sq. m ?**

<hint>

Sol :