Surface Areas and Volumes: 9 Math
NCERT Exercise 13.5: 9th math
Important Formula
Volume of a Cuboid = Length × Breadth × height
Or, Volume of a Cuboid `=lxxbxxh`
Where, `l` = length, b = breadth and h = height of the cuboid.
Volume of a Cube = (edge)3
Or Volume of a Cube = a3
Where, a = edge of cube.
NCERT Exercise 13.5 Questions and Solution
Surface Areas And Volumes Class nine Math NCERT 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?
Solution
Given, Length of the matchbox = 4 cm
Breadth of the match box = 2.5 cm
And, height of the match box = 1.5 cm
And, total number of matchboxes in the packet = 12
Thus, volume of packet containing matchboxes = ?
We know that, Volume of a Cuboid `=lxxbxxh`
Therefore, volume of given matchbox
= 4 cm × 2.5 cm × 1.5 cm
= 10.0 cm2 × 1.5 cm
= 15 cm3
Thus, volume of one given matchbox = 15 cm3
Now, volume of 12 such matchboxes = 15 cm3 × 12
= 180 cm3
Thus, volume of the box containing 12 given boxes = 180 cm3 Answer
Surface Areas And Volumes Class nine Math NCERT Exercise 13.5 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`)
Solution
Given, Length of the water tank = 6 m
And, Breadth of the water tank = 5 m
And, Height of the water tank = 4.5 m
Thus, maximum volume of water hold by tank = ?
Here, maximum volume of water hold by tank = volume of tank
Now, we know that, Volume of a Cuboid = length × breadth × height
Thus, Volume of given tank
= 6 m × 5 m × 4.5 m
= 30 m2 × 4.5 m
=135 m 3
Thus volume of the given tank = 135 m2
Now, since, 1 m3 = 1000 Litre
Therefore, 135 m3 = 135 × 1000 Litres
= 135000 `l`
Therefore, given tank can hold 135000 litres of water Answer
Surface Areas And Volumes Class nine Math NCERT Exercise 13.5 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
Given, Length of the cubical vessel (`l`) = 10 m
Breadth of the cubical vessel (b) = 8 m
And volume of liquid hold by given vessel = 380 cubic meter
Therefore, Height to hold the given volume of liquid by given vessel (h) = ?
Here, volume of the liquid hold by vessel = volume of the vessel
Volume = 380 m3
We know that, volume of the vessel = length × breadth × height
⇒ 380 m3 = 10 m × 8 m × height
⇒ 380 m3 = 80 m2 h
`=>h = (380\ m^3)/(80\ m^2)`
⇒ height (h) = 4.75 m
Thus, height of the vessel to hold given volume of liquid = 4.75 m Answer
Surface Areas And Volumes Class nine Math NCERT Exercise 13.5 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 m2.
Solution
Given, Length of the pit (`l`) = 8 m
And, breadth of the pit (b) = 6 m
And, Depth of the pit (h) = 3 m
Rate of digging = Rs.30 per m3
Therefore, cost of digging of given cuboidal pit = ?
We know that, volume of a cuboid `=lxxbxxh`
Therefore, volume of the given cuboid = 8 m × 6 m × 3 m
⇒ Volume of the given cuboid = 144 m3
Now, since to dig 1 m3, cost = Rs 30
Therefore, to dig 144 m3 = Rs 30 × 144
= Rs 4320.00
Thus, cost of digging of given pit = Rs 4320.00 Answer
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