Surface Area and Volume of a Cuboid and Cube- 1 RD Sharma Solutions | Mathematics (Maths) Class 9 PDF Download

 Page 1


Q u e s t i o n : 1
Find the lateral surface area and total surface area of a cuboid of length 80 cm, breadth 40 cm and height 20 cm.
S o l u t i o n :
Dimensions are given as
Length 
Breadth 
Height 
We have to find lateral surface area and total area
Hence its, lateral surface area,
Total surface area,
The lateral surface area of the cuboids is  and total surface area of it is .
Q u e s t i o n : 2
Find the lateral surface area and total surface area of a cube of edge 10 cm.
S o l u t i o n :
Edge of the given cube, 
We have to find lateral and total surface area
Lateral surface area,
Total surface area,
The lateral surface area of the cube is  and its total surface area is .
Q u e s t i o n : 3
Find the ratio of the total surface area and lateral surface area of a cube.
Page 2


Q u e s t i o n : 1
Find the lateral surface area and total surface area of a cuboid of length 80 cm, breadth 40 cm and height 20 cm.
S o l u t i o n :
Dimensions are given as
Length 
Breadth 
Height 
We have to find lateral surface area and total area
Hence its, lateral surface area,
Total surface area,
The lateral surface area of the cuboids is  and total surface area of it is .
Q u e s t i o n : 2
Find the lateral surface area and total surface area of a cube of edge 10 cm.
S o l u t i o n :
Edge of the given cube, 
We have to find lateral and total surface area
Lateral surface area,
Total surface area,
The lateral surface area of the cube is  and its total surface area is .
Q u e s t i o n : 3
Find the ratio of the total surface area and lateral surface area of a cube.
S o l u t i o n :
Let the length of the edge of the cube be
We have to find the ratio of total surface area and lateral surface area
Total surface area of the cube,
Lateral surface area of the cube,
The desired ratio,
The ratio of the total surface area and the lateral surface area of a cube is .
Q u e s t i o n : 4
Marry wants to decorate her Christmas tree.. She wants to place the tree on a wooden block covered with coloured
paper with picture of Santa Claus on it. She must know the exact quantity of paper to buy for this purpose. If the box
has length, breadth and height as 80 cm, 40 cm and 20 cm respectively. How many square sheets of paper of side
40 cm would she require?
S o l u t i o n :
The dimensions of the cubical block are,
We are asked to find the number of square sheet paper whose side is 40 cm
Let the total surface area of the block be .
So, Mary would require in total  of colored paper.
But the paper is available in square sheets of side,
Area of a single square sheet,
The number of square sheets required=
Page 3


Q u e s t i o n : 1
Find the lateral surface area and total surface area of a cuboid of length 80 cm, breadth 40 cm and height 20 cm.
S o l u t i o n :
Dimensions are given as
Length 
Breadth 
Height 
We have to find lateral surface area and total area
Hence its, lateral surface area,
Total surface area,
The lateral surface area of the cuboids is  and total surface area of it is .
Q u e s t i o n : 2
Find the lateral surface area and total surface area of a cube of edge 10 cm.
S o l u t i o n :
Edge of the given cube, 
We have to find lateral and total surface area
Lateral surface area,
Total surface area,
The lateral surface area of the cube is  and its total surface area is .
Q u e s t i o n : 3
Find the ratio of the total surface area and lateral surface area of a cube.
S o l u t i o n :
Let the length of the edge of the cube be
We have to find the ratio of total surface area and lateral surface area
Total surface area of the cube,
Lateral surface area of the cube,
The desired ratio,
The ratio of the total surface area and the lateral surface area of a cube is .
Q u e s t i o n : 4
Marry wants to decorate her Christmas tree.. She wants to place the tree on a wooden block covered with coloured
paper with picture of Santa Claus on it. She must know the exact quantity of paper to buy for this purpose. If the box
has length, breadth and height as 80 cm, 40 cm and 20 cm respectively. How many square sheets of paper of side
40 cm would she require?
S o l u t i o n :
The dimensions of the cubical block are,
We are asked to find the number of square sheet paper whose side is 40 cm
Let the total surface area of the block be .
So, Mary would require in total  of colored paper.
But the paper is available in square sheets of side,
Area of a single square sheet,
The number of square sheets required=
Mary would require  square sheets of paper.
Q u e s t i o n : 5
The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the
walls of the room and the ceiling at the rate of Rs. 7.50 m
2
.
S o l u t i o n :
Dimensions of the room are,
Let,
S The total surface area to whitewash
A
1
 The lateral surface area of the room
A
2 
The surface area of ceiling
R The rate of whitewashing per 
We know that,
We are asked to find the cost of whitewashing
Now, the total surface area to whitewash,
Total cost of whitewashing,
Hence the cost of whitewashing the room and the ceiling is .
Q u e s t i o n : 6
Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of the
sum of the surfaces areas of the three cubes.
S o l u t i o n :
Let,
Side of each cube
Page 4


Q u e s t i o n : 1
Find the lateral surface area and total surface area of a cuboid of length 80 cm, breadth 40 cm and height 20 cm.
S o l u t i o n :
Dimensions are given as
Length 
Breadth 
Height 
We have to find lateral surface area and total area
Hence its, lateral surface area,
Total surface area,
The lateral surface area of the cuboids is  and total surface area of it is .
Q u e s t i o n : 2
Find the lateral surface area and total surface area of a cube of edge 10 cm.
S o l u t i o n :
Edge of the given cube, 
We have to find lateral and total surface area
Lateral surface area,
Total surface area,
The lateral surface area of the cube is  and its total surface area is .
Q u e s t i o n : 3
Find the ratio of the total surface area and lateral surface area of a cube.
S o l u t i o n :
Let the length of the edge of the cube be
We have to find the ratio of total surface area and lateral surface area
Total surface area of the cube,
Lateral surface area of the cube,
The desired ratio,
The ratio of the total surface area and the lateral surface area of a cube is .
Q u e s t i o n : 4
Marry wants to decorate her Christmas tree.. She wants to place the tree on a wooden block covered with coloured
paper with picture of Santa Claus on it. She must know the exact quantity of paper to buy for this purpose. If the box
has length, breadth and height as 80 cm, 40 cm and 20 cm respectively. How many square sheets of paper of side
40 cm would she require?
S o l u t i o n :
The dimensions of the cubical block are,
We are asked to find the number of square sheet paper whose side is 40 cm
Let the total surface area of the block be .
So, Mary would require in total  of colored paper.
But the paper is available in square sheets of side,
Area of a single square sheet,
The number of square sheets required=
Mary would require  square sheets of paper.
Q u e s t i o n : 5
The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the
walls of the room and the ceiling at the rate of Rs. 7.50 m
2
.
S o l u t i o n :
Dimensions of the room are,
Let,
S The total surface area to whitewash
A
1
 The lateral surface area of the room
A
2 
The surface area of ceiling
R The rate of whitewashing per 
We know that,
We are asked to find the cost of whitewashing
Now, the total surface area to whitewash,
Total cost of whitewashing,
Hence the cost of whitewashing the room and the ceiling is .
Q u e s t i o n : 6
Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of the
sum of the surfaces areas of the three cubes.
S o l u t i o n :
Let,
Side of each cube
Surface area of each cube
So, 
Hence,
Sum of surface areas of three cubes,
The length (say l) of the newly formed cuboids is;
Its breadth (say b) and height (say h) will be the same as that of each cube.
Total surface area of the new cuboids is;
Required Ratio,
The total surface area of the new cuboids to that of the sum of the surface area of the three cubes is 
Q u e s t i o n : 7
A 4 cm cube is cut into 1 cm cubes. Calculate the total surface area of all the small cubes.
S o l u t i o n :
We can define the following notations as follows
Side of cube
Volume of  cube
Side of cube
Volume of cube
Let;
Number of cubes formed
Surface area of a single small cube
We know,
Page 5


Q u e s t i o n : 1
Find the lateral surface area and total surface area of a cuboid of length 80 cm, breadth 40 cm and height 20 cm.
S o l u t i o n :
Dimensions are given as
Length 
Breadth 
Height 
We have to find lateral surface area and total area
Hence its, lateral surface area,
Total surface area,
The lateral surface area of the cuboids is  and total surface area of it is .
Q u e s t i o n : 2
Find the lateral surface area and total surface area of a cube of edge 10 cm.
S o l u t i o n :
Edge of the given cube, 
We have to find lateral and total surface area
Lateral surface area,
Total surface area,
The lateral surface area of the cube is  and its total surface area is .
Q u e s t i o n : 3
Find the ratio of the total surface area and lateral surface area of a cube.
S o l u t i o n :
Let the length of the edge of the cube be
We have to find the ratio of total surface area and lateral surface area
Total surface area of the cube,
Lateral surface area of the cube,
The desired ratio,
The ratio of the total surface area and the lateral surface area of a cube is .
Q u e s t i o n : 4
Marry wants to decorate her Christmas tree.. She wants to place the tree on a wooden block covered with coloured
paper with picture of Santa Claus on it. She must know the exact quantity of paper to buy for this purpose. If the box
has length, breadth and height as 80 cm, 40 cm and 20 cm respectively. How many square sheets of paper of side
40 cm would she require?
S o l u t i o n :
The dimensions of the cubical block are,
We are asked to find the number of square sheet paper whose side is 40 cm
Let the total surface area of the block be .
So, Mary would require in total  of colored paper.
But the paper is available in square sheets of side,
Area of a single square sheet,
The number of square sheets required=
Mary would require  square sheets of paper.
Q u e s t i o n : 5
The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the
walls of the room and the ceiling at the rate of Rs. 7.50 m
2
.
S o l u t i o n :
Dimensions of the room are,
Let,
S The total surface area to whitewash
A
1
 The lateral surface area of the room
A
2 
The surface area of ceiling
R The rate of whitewashing per 
We know that,
We are asked to find the cost of whitewashing
Now, the total surface area to whitewash,
Total cost of whitewashing,
Hence the cost of whitewashing the room and the ceiling is .
Q u e s t i o n : 6
Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of the
sum of the surfaces areas of the three cubes.
S o l u t i o n :
Let,
Side of each cube
Surface area of each cube
So, 
Hence,
Sum of surface areas of three cubes,
The length (say l) of the newly formed cuboids is;
Its breadth (say b) and height (say h) will be the same as that of each cube.
Total surface area of the new cuboids is;
Required Ratio,
The total surface area of the new cuboids to that of the sum of the surface area of the three cubes is 
Q u e s t i o n : 7
A 4 cm cube is cut into 1 cm cubes. Calculate the total surface area of all the small cubes.
S o l u t i o n :
We can define the following notations as follows
Side of cube
Volume of  cube
Side of cube
Volume of cube
Let;
Number of cubes formed
Surface area of a single small cube
We know,
And;
The number of cubes formed,
Total surface area of all the small cubes formed
The total surface area of all the small cubes is .
Q u e s t i o n : 8
The length of a hall is 18 m and the width 12 m. The sum of the areas of the floor and the flat roof is equal to the
sum of the areas of the four walls. Find the height of the hall.
S o l u t i o n :
The hall is cubical.
Let,
Length of the cuboids
Breadth of the cuboids
Height of the cuboids
We have,
We need to find the Height of the hall
It is given that,
The sum of the areas of the floor and the flat roof is equal to the sum of the areas of the four walls
Using abbreviations, we can write the same as,
Height of the wall is .