NCERT Solutions Class 9 Mathematics Surface Areas and Volumes Exercise 13.5

Exercise 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?

Answer :

Measures of matchbox (cuboid) is 4 cm * 2.5 cm * 1.5 cm          

⇒ l = 4 cm, b = 2.5 cm and h = 1.5 cm        

Now, Volume of matchbox = l * b * h          

                                                  = 4 * 2.5 * 1.5

                                                  = 15 cm³

So, volume of 12 boxes = 12 * 15 = 180 cm³

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 hold?  (1 m³ = 1000 l)

Answer :

Here, Length (l) = 6 m, Breadth (b) = 5 m, Depth (h) = 4.5 m                

Capacity = l * b * h = 6 * 5 * 4.5 m³                    

Since 1 m³ can hold 1000 l.         

So, 135 m³ can hold 135 * 1000 l = 135000 l of water.         

Hence, the required amount of water in the tank = 135000 l.

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 liquid?

Answer :

Given, Length (l) = 10 m, Breadth (b) = 8 m, Volume (v) = 380 m³    

Let height of the cuboid be h.          

Since, volume of a cuboid = l × b × h       

⇒ 10 * 8 * h = 380      

⇒ 80h = 380                     

⇒ h = 380/80 = 4.75

Thus, the required height of the liquid = 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 m³.

Answer :

Given, Length (l) = 8 m, Breadth (b) = 6 m, Depth (h) = 3 m          

Now, Volume of the cuboidal pit = l * b * h

                                                           = 8 * 6 * 3

                                                           = 144 m³

Since, rate of digging the pit is Rs. 30 per m³.          

So, cost of digging = Rs. 30 * 144 = Rs. 4320

Question : 5: The capacity of 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 in.

Answer :

Length of the tank (l) = 2.5 m, Depth of the tank (h) = 10 m          

Let breadth of the tank = b m          

Now, Volume (capacity) of the tank= l * b * h = 2.5 * b * 10 = 25b m³                           

But the capacity of the tank = 50000 l = 50000/1000 m³ = 50 m³          

So, 25b = 50

⇒ b = 50/25

⇒ b = 2

Thus, the depth of the tank = 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?

Answer :

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

Volume of the tank = l * b * h = 20 * 15 * 6 = 1800 m³          

Since 1 m³ = 1000 l         

So, Capacity of the tank = 1800 * 1000 = 1800000 l                

Village population = 4000          

Since, 150 l of water is required per head per day.          

So, the amount of water is required per day = 150 * 4000 l.          

Let the required number of days = x     

⇒ 4000 * 150 * x = 1800000          

⇒ x = (1800000)/(4000 * 150)

⇒ x = 3

Thus, the required number of days is 3

Question : 7: A godown measures 60 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.

Answer :

Volume of the godown = 60 * 25 * 10 m³          

Volume of a crate = 1.5 * 1.25 * 0.5 m³

Let the required number of wooden create be n

So, n * 1.5 * 1.25 * 0.5 = 60 * 25 * 10

⇒ n = (60 * 25 * 10)/( 1.5 * 1.25 * 0.5)

⇒ n = (60 * 25 * 10 * 10 * 100 * 10)/(15 * 125 * 5)

⇒ n = (4 * 10 * 2 * 100 * 10)/5

⇒ n = 4 * 10 * 2 * 100 * 2

⇒ n = 16000

Hence, the maximum number of wooden crates is 16000.