Ncert Solutions For Class 9 Maths Ex 13.1

Ncert Solutions For Class 9 Maths Chapter 13 Ex 13.1

QUESTIONS-:

1. A matchbox measures 5cm × 1cm × 3.5cm. Determine the volume of a packet containing 14 such boxes.

Soln.

Given the dimension of the matchbox = 5cm × 1cm × 3.5cm

Let us assume, l = 5cm, b = 1cm, h = 3.5cm

As we know that, Volume of one matchbox = (l × b × h)

= (5×1×3.5)cm3=17.5cm3

Thevolumeofapacketcontaining14suchboxes=(17.5×14)cm3=245cm3

 

2. A cuboidal water tank is 10 m long, 2 m wide and 7.5 m deep. How many litres of water can it hold? (1m3 = 1000 l)

Soln.

Dimensions of water tank = 10m × 2m × 7.5m

Let us assume, l = 10m, b = 2m, h = 7.5m

Therefore Volume of the tank = (l×b×h)m3

= (10×2×7.5)m3=150m3

Hence, the tank can hold = 150 x 1000 litres = 150000 litres of water.

 

3. A cuboidal vessel is 25 m long and 12 m wide. Determine the height that must be made to hold 400 cubic metres of a liquid.

Soln.

Given, Length = 25 m , Breadth = 12 m and Volume = 400m3

As we know, Volume of cuboid = Length x Breadth x Height

Therefore, Height = Volume of cuboid/(Length × Breadth)
= 40025×12m=1.33m

 

4.  Find the value of digging a cuboidal pit 15 m long, 5 m broad and 3 m deep at the rate of Rs.50 per m3.

Soln.

Here, length = 15m, breadth = 5m and height = 3m

As we know that, Volume of the pit = (l×b×h)m3

= (15×5×3)m3=225m3

The rate of digging is = Rs.50 per m3

∴ The total value of digging the pit = Rs.(225 x 50)

= Rs.11250

 

 

5. The capacity of a cuboidal tank is 2,10000 litres of water. Calculate the breadth, given that the length is 3.5m and depth is 20m.

Soln.

Given, length = 3.5m, depth = 15m and volume = 30000 litres

As we know that, 1m3=1000litres

210000litres=2100001000m3= 2101m3

Breadth = volumeofcuboidlength×depth

= 210(3.5×20)m

= 3m

 

6. A village, with a population of 6000, requires 200 litres of water per head per day. It has a tank measuring 30m × 25m × 8m. Justify the number of days that will take to empty the water tank.

Soln.

Given, the dimension of the tank = 30m × 25m × 8m

So, l = 30m, b = 25m and h = 8m

As we know that, the total capacity of the tank = (30×25×8)m3=6000m3

Water required for a single person per day = 200 litres

The requirement of water for 6000 person in a single day = (6000 x 200) litres

= (6000×200)1000=1200m3

Hence, the number of days the water will last = (the capacity of the tank /water required per day) = (60001200)=5

∴ The water lasts for 5 days.

 

7. A warehouse measures 50m × 35m × 25m. Calculate the maximum number of wooden boxes each measuring 2.5m × 1.5m × 1m that can be stored in the warehouse.

Soln.

Given the dimensions of the warehouse = 50m x 35m x 25m

As we know that, the volume of the warehouse will be = (lbh)m3

= (50×35×25)m3=43750m3

Now, the dimension of box = 2.5m x 1.5m x 1m

Similarly, volume of 1 box = (2.5×1.5×1)m3=3.75m3

Hence, Number of box that can be stored =  volume of warehouse / volume of 1 box = 437503.75=11666.666=11666

 

8. A solid cuboid having side 20 cm is cut into 16 cubes of equal volume. Calculate the side of the new cuboid and also calculate the ratio between their surface areas.

Soln.

Here the edge of the cube = 20cm

So, Volume of the cuboid = (edge)3cm3

= (20×20×20)cm3=8000cm3

Now, The number of smaller cube = 16

So, the volume of 1 small cube = 800016cm3=500cm3

Let us assume the side of small cube as ‘p’

p3=500p=7.937(approx)

Hence, the surface area the cube = 7.937(side)2

Therefore, the ratio of their surface area

= (7.937 x 20 x 20)/(7.937 x 7.937 x 7.937)

= 401.585 = 40 :1.585

 

9. A river 5 m deep and 60 m wide is flowing at a rate of 6 km per hour. Estimate the amount of water that will fall into the sea in a minute.

Soln.

Given, Depth (h) = 5m

Width (b) = 60m

So, the rate of flow of water (l) = 6km per hour= (600060)mperminute=100mperminute

Therefore, the volume of water flowing into the sea in a minute = lbhm3

(100×60×5)m3=30000m3