NCERT Class 9 Maths Solutions Chapter - 13 Surface Areas and Volumes, Ex - 13.5

Ex - 13.5

Question 1.  A matchbox measures 4 cm  2.5 cm  1.5 cm. What will be the volume of a packet containing 12 such boxes?

Solution

A matchbox is cuboidal in shape.
Volume of 1 match box = l  b  h = (4  2.5  1.5)  = 15  

Volume of the packet containing 12 such matchboxes = 12  15  =180 

Question 2.  A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How, many litres of water can it holds? (1  = 1000l)

Solution

Volume of tank = l  b  h = (6  5  4.5)  = 135 

  It is given that:
 1  = 1000 litres

  
 Thus, the tank can hold 135000 litres of water.

Question 3.  A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?

Solution

Let height of cuboidal vessel be h.
Length (l) of vessel = 10 m
Width (b) of vessel = 8 m
Volume of vessel = 380 
 l  b  h = 380 

     
 10  8  h = 380
 h = 4.75
  
 Thus, the height of the vessel should be 4.75 m.

Question 4.  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 .

Solution

Length (l) of the cuboidal pit = 8 m
Width (b) of the cuboidal pit = 6 m
 Depth (h) of the cuboidal pit = 3 m
Volume of the cuboidal pit = l  b  h = (8  6  3)  = 144    

Cost of digging 1  = Rs 30
Cost of digging 144  = Rs (144 30) = Rs 4320

Question 5.  The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m.

Solution

Let the breadth of the tank be 'b' m.
Length (l) of the tank = 2.5 m
Depth (h) of the tank = 10 m

Volume of tank = l  b  h = (2.5  b  10)  = 25b 
  
Capacity of tank = 25b  = 25000 b litres
 25000 b = 50000    (Given)

  Thus, the breadth of the tank is 2 m.

Question 6.  A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m  15 m  6 m. For how many days will the water of this tank last?

Solution

Length (l) of the cuboidal tank = 20 m 
Breadth (b) of the cuboidal tank = 15 m 
Height (h) of the cuboidal tank = 6 m

Capacity of tank = l  bh    = (20  15  6)  = 1800  = 1800000 litres

Water consumed by people of village in 1 day = 4000  150 litres = 600000 litres

Let water of this tank lasts for n days.
Water consumed by all people of village in n days = capacity of tank
n  600000 = 1800000
n = 3    
Thus, the water of tank will last for 3 days.

Question 7.  A godown measures 40 m  25 m  10 m. Find the maximum number of wooden crates each measuring 1.5 m  1.25 m  0.5 m that can be stored in the godown.

Solution

Length  of the godown = 40 m
    Breadth  of the godown = 25 m
    Height  of the godown = 10 m

Volume of godown = l₁  b₁ h₁ = (40  25  10)  = 10000   

    Length  of a wooden crate = 1.5 m
    Breadth  of a wooden crate = 1.25 m
    Height  of a wooden crate = 0.5 m

Volume of a wooden crate =      = (1.5  1.25  0.5) m³ = 0.9375 

Let n wooden crates be stored in the godown.
Volume of n wooden crates = volume of godown
0.9375  n = 10000

Thus, 10666 number of wooden crates can be stored in godown.

Question 8.  A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.

Solution

Side (a) of the cube = 12 cm
Volume of the cube = a³= (12 cm)³ = 1728

Let the side of each smaller cube be l.

Volume of each smaller cube  

 l = 6 cm
Thus, the side of each smaller cube is 6 cm.
Ratio between surface areas of the cubes =  

  
So, the required ratio between surface areas of the cubes is 4 : 1.

Question 9.  A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?

Solution

Rate of water flow = 2 km per hour  
Depth (h) of river = 3 m
Width (b) of river = 40 m
Volume of water flowed in 1 min  
Thus, in 1 minute 4000  water will fall into the sea.

Ex-13.4

Ex-13.6