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NCERT Solutions Class 9 Maths Chapter 13 Surface area and Volume Exercise 13.5

Introduction:

In this exercise/article we will learn about Surface Area And Volume. Volume of cuboid and cube .If an object is solid, then the space occupied by such an object is measured, and it termed the Volume of the object. On the other hand, if the object is hollow, then interior is empty, and can be filled with air, or some liquid that will take the shape of its container. In this case, the volume of the substance that can fill the interior is called the capacity of the container. In short, the volume of an object is the measure of the space it occupies, and the capacity of an object is the volume of substance its interior can accommodate.

Class 9 Maths Chapter 13 Surface Area And Volume :

Class 9 Maths Exercise 13.5 (Page-228)

Q1. A matchbox measured 4 cm × 2.5 cm × 1.5 cm. What will be the volume of a packet containing 12 such boxes?

Solution :

According to the question,

Given, Length = 4 cm

Breadth = 2.5 cm

Height = 1.5 cm

So, volume of a matchbox = length × breadth × height

= 4 × 2.5 × 1.5

= 15 cm3

∴ Volume of a matchbox = 15 cm3

After that, the volume of a packet containing 12 boxes = 15 × 12

= 180 cm3

∴ The volume of a packet containing 12 boxes = 180 cm3 .

Q2. A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many liters of water can it hold? ( 1 m3 = 1000 l )

Solution :

According to the question,

Given, Length = 6 m

Breadth = 5 m

Height = 4.5 m

So, volume of a cuboidal water tank = length × breadth × height

= 6 × 5 × 4.5

= 135 m3

∴ volume of a cuboidal water tank = 135 m3

According to the question 1 m3 = 1000 l

135 m3 = 135 × 1000 l =135000 l

∴ Cuboidal water tank Hold upto 135000 l.

Q3. A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic meters of a liquid?

Solution :

According to the question,

Given, Length = 10 m

Breadth = 8 m

Volume of a cuboidal vessel = 380 m3

So, volume of a cuboidal vessel = length × breadth × height

⇒ 380 = 10 × 8 × h

⇒ 380 = 180h

⇒ \(\displaystyle \frac{{380}}{{80}}\) = h

⇒ 4.75 m3 = h

∴ 4.75 m3 high must it be made to hold .

Q4. 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 .

Solution :

According to the question,

Given, Length = 8 m

Breadth = 6 m

Height = 3 m

So, volume of a cuboidal pit = length × breadth × height

= 8 × 6 × 3

= 144 m3

∴ volume of cuboidal pit = 144 m3

Now, the cost of digging a cuboidal pit 1m3 = Rs 30

The cost of digging a cuboidal pit 144 m3 = Rs 144 × 30

= Rs 4320

∴ The cost of digging the cuboidal pit = Rs 4320 .

Q5. The capacity of a cuboidal tank is 50000 liters of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m.

Solution :

According to the question,

Given, Length = 2.5 m

Height = 10 m

Volume of a cuboidal tank = 50000 liters

= 50 m3 [ converted l to m ]

So, volume of a cuboidal tank = length × breadth × height

⇒ 50 = 2.5 × 10 × b

⇒ 50 = 25b

⇒ \(\displaystyle \frac{{50000}}{{25}}\) = b

⇒ 2 m = b

∴ The breadth of the tank = 2 m .

Q6. 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 be water of this tank last?

Solution :

According to the question,

Given, Length = 20 m

Breadth = 15 m

Height = 6 m

So, volume of a water tank = length × breadth × height

= 20 × 15 × 6

= 1800 m3

⇒ 1800 × 1000 = 1800000 litres [ convert m3 to litres ]

Now, Requires of water per head per day = 150 litres

So, Requires of water 4000 person for per day = 150 × 4000

= 600000 litres

∴ Number of days to consumed all people water of tank = \(\displaystyle \frac{{1800000}}{{600000}}\)

= 3 days

∴ 3 days will be water of this tank last .

Q7. 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 :

According to the question,

Given, ( godown ) Length = 40 m

Breadth = 25 m

Height = 10 m

So, volume of a godown = length × breadth × height

= 40 × 25 × 10

= 10000 m3

∴ Volume of a godown = 10000 m3

Given, ( wooden craft ) Length = 1.5 m

Breadth = 1.25 m

Height = 0.5 m

So, volume of a wooden craft = length × breadth × height

= 1.5 × 1.25 × 0.5

= 0.9375 m3

∴ Volume of a wooden craft = 0.9375 m3

Now, the maximum number of wooden crates that can be stored in the godown = \(\displaystyle \frac{{10000}}{{0.9375}}\)

= 10666.66 crates

∴ The maximum number of wooden crates that can be stored in the godown = 10666 crates .

Q8. 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 :

According to the question,

Given, Big cube side = 12 cm

So, volume of a cube = a3

= 12 × 12 × 12

= 1728 cm3

∴ Big cube side = 1728 cm3

Now, volume of each small cube = \(\displaystyle \frac{{1728}}{8}\) cm3

= 216 cm3

(i) Side of each small cube = \(\displaystyle \sqrt{{216}}\) cm3

= 6 cm

(ii) The ratio between their surface areas = \(\displaystyle \frac{{Surface\,area\,of\,big\,cube}}{{Surface\,area\,of\,small\,cube}}\)

= \(\displaystyle \frac{{6{{a}^{2}}}}{{6{{a}^{2}}}}\)

= \(\displaystyle \frac{{6\,\times \,12\,\times \,12}}{{6\,\times \,6\,\times \,6}}\)

= \(\displaystyle \frac{{864}}{{216}}\)

= \(\displaystyle \frac{1}{4}\)

= 1 : 4

∴ The ratio of surface areas between big cube and small cube surface areas = 1 : 4 .

Q9. A river 3 m deep and 40 m wide if flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute ?

Solution :

According to the question,

Given, Height = 3 m

breadth = 40 m

Let Length = 2 km per hour

= 2000 m per hour [ convert km per hour to m per hour ]

So, volume of water flowed 1 hour = length × breadth × height

= 2000 × 40 × 3

= 240000 m3

Now, volume of water flowed 1 minute = \(\displaystyle \frac{{240000}}{{60}}\) m3

= 4000 m3

∴ 4000 m3 water will fall into the sea in a minute .

Class 9 Maths Chapter 13 Surface Area And Volume :

NCERT Solutions Class 9 Maths Chapter 13 Surface Area And Volume Exercise 13.5

NCERT Solutions Class 9 Maths Chapter 13 Surface area and Volume Exercise 13.5

Introduction:

Class 9 Maths Exercise 13.5 (Page-228)

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