The document Ex 13.5 NCERT Solutions- Surface Areas and Volumes Class 9 Notes | EduRev is a part of the Class 9 Course Class 9 Mathematics by Full Circle.

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**Question 1. A matchbox measures 4 cm x 2.5 cm. x 1.5 cm. What will be the volume of a packet containing 12 such boxes? Solution:** Measures of matchbox (cuboid) is 4 cm x 2.5 cm x 1.5 cm

â‡’ l = 4 cm, b = 2.5 cm and h = 1.5 cm

âˆ´ Volume of matchbox = (l x b) x h = [4 cm x 2.5 cm] x 1.5 cm

= 15 cm^{3 }

â‡’ Volume of 12 boxes = 12 x 15 cm^{3} = 180 cm^{3}

**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 m ^{3} = 1000 l) Solution:** Here, Length (l)= 6 m

Breadth (b) = 5 m

Depth (h) = 4.5 m

âˆ´ Capacity = l x b x h = 6 x 5 x 4.5 m

= 6 x 5 x (45/10) m

âˆµ 1 m^{3} can hold 1000 l.

âˆ´ 135 m^{3} can hold (135 x 1000 l = 135000 l) of water.

âˆ´ 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? Solution: **Length (l) = 10 m

Breadth (b) = 8 m

Volume (v) = 380 m

Let height of the cuboid be â€˜hâ€™.

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

âˆ´ Volume of the cuboidal vessel = 10 x 8 x h m

â‡’ 80h = 380

h= 380/80 = 19/4 m = 4.75 m

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 **â‚¹** 30 per m ^{3}. Solution: **Length (l)= 8 m

Breadth (b) = 6 m

Depth (h) = 3 m

âˆ´ Volume of the cuboidal pit = l x b x h = 8 x 6 x 3 m

= 144 m

Since, rate of digging the pit is â‚¹ 30 per m

âˆ´ Cost of digging = â‚¹ 30 x 144 = â‚¹ 4320

Solution:

Depth of the tank (h) = 10 m

Let breadth of the tank = b m

âˆ´ Volume (capacity) of the tank = l x b x h = 2.5 x b x 10 m

But the capacity of the tank = 50000 l = 50 m

âˆ´ 25b = 50 m

â‡’ b= (50/25) m = 2 m

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 x 15 m x 6 m. For how many days will the water of this tank last? Solution:** Length of the tank (l) = 20 m

Breadth of the tank (b) = 15 m

Height of the tank (h) = 6 m

âˆ´ Volume of the tank = l x b x h = 20 x 15 x 6 m

Since 1 m

âˆ´ Capacity of the tank = 1800 x 1000 l = 1800000 l

Village population = 4000

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

âˆ´ Amount of water is required per day = 150 x 4000 l.

Let the required number of days = x

Thus, the required number of days is 3.

**Question 7. A godown measures 60 m x 25 m x 10 m. Find the maximum number of wooden crates each measuring 1.5 m x 1.25 m x 0.5 m that can be stored in the godown. Solution:**

**volume of the godown = **60x 25 x 10 m^{3}

Volume of a crate = 1.5 x 1.25 x 0.5 m^{3}

Let the required number of crates is â€˜nâ€™.

= 16000

**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 of the given cube = 12 cm

âˆ´ Volume of the given cube = (side)

Side of the smaller cube:

Let the side of the new (smaller) cube = n

â‡’ Volume of smaller cube = n

â‡’ Volume of 8 smaller cubes = 8n

Thus, the required side of the new (smaller) cube is 6 cm.

Ratio between surface areas:

Surface area of the given cube = 6 x (side)^{2} = 6 x 122 cm^{2 }

= 6 x 12 x 12 cm^{2}

Surface area of one smaller cube = 6 x (side)^{2 }= 6 x 62 cm^{2 }

= 6 x 6 x 6 cm^{2}

âˆ´ Surface area of 8 smaller cubes = 8 x 6 x 6 x 6 cm^{2}

**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: **The water flowing in a river can be considered in the form of a cuboid.

Such that Length (l) = 2 km = 2000 m

Breadth (b) = 40 m

Depth (h) = 3 m

âˆ´ Water volume (volume of the cuboid so formed) = l x b x h = 2000 x 40 x 3 m^{3}

Now, volume of water fallowing in 1 hr (= 60 minutes) = 2000 x 40 x 3 m^{3}

âˆ´ Volume of water that will fall in 1 minute

**VOLUME OF A CYLINDER**

For a right circular cylinder, if â€˜râ€™ be the base radius and â€˜hâ€™ be its height then,

Volume = Base area x height

= Ï€r^{ 2}h

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