Surface Area and Volume of a Cuboid and Cube- 2 RD Sharma Solutions | Mathematics (Maths) Class 9 PDF Download

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Q u e s t i o n : 2 0
A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold?
S o l u t i o n :
Dimensions of the water tank, l = 6 m, b = 5 m, h = 4.5 m
We need to find the capacity of the tank
Capacity of the tank,
The tank can hold  of water.
Q u e s t i o n : 2 1
A cubical vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?
S o l u t i o n :
We have,
Length of the vessel
Page 2


 
       
      
   
   
 
    
Q u e s t i o n : 2 0
A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold?
S o l u t i o n :
Dimensions of the water tank, l = 6 m, b = 5 m, h = 4.5 m
We need to find the capacity of the tank
Capacity of the tank,
The tank can hold  of water.
Q u e s t i o n : 2 1
A cubical vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?
S o l u t i o n :
We have,
Length of the vessel
Width of the vessel
Capacity of the vessel
Let:  Minimum required height of the vessel
So,
Thus, to hold of liquid, the vessel must be minimum high.
Q u e s t i o n : 2 2
Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m
3
.
S o l u t i o n :
We have, the dimensions of the cubical pit are,
Length
Breadth
Depth
Rate of digging
Volume of the pit,
The cost of digging,
The cost of digging the pit is .
Q u e s t i o n : 2 3
If the areas of three adjacent faces of a cuboid are 8 cm
2
, 18 cm
3 
and 25 cm
3
. Find the volume of the cuboid.
S o l u t i o n :
We know that, areas of three adjacent faces of the cuboid are  respectively.
Where,
Length of the cuboid
Breadth of the cuboid
Height of the cuboid
Page 3


 
       
      
   
   
 
    
Q u e s t i o n : 2 0
A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold?
S o l u t i o n :
Dimensions of the water tank, l = 6 m, b = 5 m, h = 4.5 m
We need to find the capacity of the tank
Capacity of the tank,
The tank can hold  of water.
Q u e s t i o n : 2 1
A cubical vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?
S o l u t i o n :
We have,
Length of the vessel
Width of the vessel
Capacity of the vessel
Let:  Minimum required height of the vessel
So,
Thus, to hold of liquid, the vessel must be minimum high.
Q u e s t i o n : 2 2
Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m
3
.
S o l u t i o n :
We have, the dimensions of the cubical pit are,
Length
Breadth
Depth
Rate of digging
Volume of the pit,
The cost of digging,
The cost of digging the pit is .
Q u e s t i o n : 2 3
If the areas of three adjacent faces of a cuboid are 8 cm
2
, 18 cm
3 
and 25 cm
3
. Find the volume of the cuboid.
S o l u t i o n :
We know that, areas of three adjacent faces of the cuboid are  respectively.
Where,
Length of the cuboid
Breadth of the cuboid
Height of the cuboid
Let,
Volume of the cuboid
We have, areas of three adjacent faces of the cuboid are  respectively,
So their product,
The volume of the cuboid is .
Q u e s t i o n : 2 4
The breadth of a room is twice its height, one half of its length and the volume of the room is 512 cu. dm. Find its
dimensions.
S o l u t i o n :
Let,
Length of the room
Breadth of the room
Height of the room
Volume of the room
We have, b = 2h, l = 2b and volume of room is 512 dm
3
We have to find the dimensions
We know that
We have, 
Therefore,
Hence, the dimensions of the cuboid are,
Page 4


 
       
      
   
   
 
    
Q u e s t i o n : 2 0
A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold?
S o l u t i o n :
Dimensions of the water tank, l = 6 m, b = 5 m, h = 4.5 m
We need to find the capacity of the tank
Capacity of the tank,
The tank can hold  of water.
Q u e s t i o n : 2 1
A cubical vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?
S o l u t i o n :
We have,
Length of the vessel
Width of the vessel
Capacity of the vessel
Let:  Minimum required height of the vessel
So,
Thus, to hold of liquid, the vessel must be minimum high.
Q u e s t i o n : 2 2
Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m
3
.
S o l u t i o n :
We have, the dimensions of the cubical pit are,
Length
Breadth
Depth
Rate of digging
Volume of the pit,
The cost of digging,
The cost of digging the pit is .
Q u e s t i o n : 2 3
If the areas of three adjacent faces of a cuboid are 8 cm
2
, 18 cm
3 
and 25 cm
3
. Find the volume of the cuboid.
S o l u t i o n :
We know that, areas of three adjacent faces of the cuboid are  respectively.
Where,
Length of the cuboid
Breadth of the cuboid
Height of the cuboid
Let,
Volume of the cuboid
We have, areas of three adjacent faces of the cuboid are  respectively,
So their product,
The volume of the cuboid is .
Q u e s t i o n : 2 4
The breadth of a room is twice its height, one half of its length and the volume of the room is 512 cu. dm. Find its
dimensions.
S o l u t i o n :
Let,
Length of the room
Breadth of the room
Height of the room
Volume of the room
We have, b = 2h, l = 2b and volume of room is 512 dm
3
We have to find the dimensions
We know that
We have, 
Therefore,
Hence, the dimensions of the cuboid are,
Length , Breadth , Height
Therefore, length is equal to 16 dm, breadth is 8 m  and Height is 4 dm.
Q u e s t i o n : 2 5
Three metal cubes with edges 6 cm, 8 cm and 10 cm respectively are melted together and formed into a single
cube. Find the volume, surface area and diagonal of the new cube.
S o l u t i o n :
Let,
Sides of the three small cubes
Volumes of the three small cubes
Side of the new cube formed
Volume of the new cube formed
Surface area of the new cube formed
Diagonal of the new cube formed
We have,
We need to find the volume, surface area and diagonal of the new cube
Now,
We know,
Page 5


 
       
      
   
   
 
    
Q u e s t i o n : 2 0
A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold?
S o l u t i o n :
Dimensions of the water tank, l = 6 m, b = 5 m, h = 4.5 m
We need to find the capacity of the tank
Capacity of the tank,
The tank can hold  of water.
Q u e s t i o n : 2 1
A cubical vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?
S o l u t i o n :
We have,
Length of the vessel
Width of the vessel
Capacity of the vessel
Let:  Minimum required height of the vessel
So,
Thus, to hold of liquid, the vessel must be minimum high.
Q u e s t i o n : 2 2
Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m
3
.
S o l u t i o n :
We have, the dimensions of the cubical pit are,
Length
Breadth
Depth
Rate of digging
Volume of the pit,
The cost of digging,
The cost of digging the pit is .
Q u e s t i o n : 2 3
If the areas of three adjacent faces of a cuboid are 8 cm
2
, 18 cm
3 
and 25 cm
3
. Find the volume of the cuboid.
S o l u t i o n :
We know that, areas of three adjacent faces of the cuboid are  respectively.
Where,
Length of the cuboid
Breadth of the cuboid
Height of the cuboid
Let,
Volume of the cuboid
We have, areas of three adjacent faces of the cuboid are  respectively,
So their product,
The volume of the cuboid is .
Q u e s t i o n : 2 4
The breadth of a room is twice its height, one half of its length and the volume of the room is 512 cu. dm. Find its
dimensions.
S o l u t i o n :
Let,
Length of the room
Breadth of the room
Height of the room
Volume of the room
We have, b = 2h, l = 2b and volume of room is 512 dm
3
We have to find the dimensions
We know that
We have, 
Therefore,
Hence, the dimensions of the cuboid are,
Length , Breadth , Height
Therefore, length is equal to 16 dm, breadth is 8 m  and Height is 4 dm.
Q u e s t i o n : 2 5
Three metal cubes with edges 6 cm, 8 cm and 10 cm respectively are melted together and formed into a single
cube. Find the volume, surface area and diagonal of the new cube.
S o l u t i o n :
Let,
Sides of the three small cubes
Volumes of the three small cubes
Side of the new cube formed
Volume of the new cube formed
Surface area of the new cube formed
Diagonal of the new cube formed
We have,
We need to find the volume, surface area and diagonal of the new cube
Now,
We know,
So, the volume, surface area and the diagonal of the new cube will be  respectively.
Q u e s t i o n : 2 6
Two cubes, each of volume 512 cm
3 
are joined end to end. Find the surface area of the resulting cuboid.
S o l u t i o n :
We have volume of each cube 
Let,
Side of each cube
The two cubes are joined together and we are asked to find the surface area of new cuboid
We know that,
When the two cubes are joined end to end,
Dimensions of the resulting cuboid are,
Length 
Breadth 
Height 
Hence, its surface area
The surface area of the resulting cuboid will be .
Q u e s t i o n : 2 7
A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edge of the two smaller cubes are
6 cm and 8 cm, find the edge of the third smaller cube.
S o l u t i o n :
Let,
Side of the cube
Volume of the cube
Sides of the three smaller cubes
Volumes of the three smaller cubes
We have,
,