Question 1. A matchbox measures 4cm×2.5cm×1.5cm. What will be the volume of a packet containing 12 such boxes?
Solution:
Given,
Dimensions of the matchbox
l = 4cm, b = 2.5cm, h = 1.5cm
As we know, a matchbox is a cuboid and, Volume of a cuboid = l×b×h
So, volume of the matchbox = 4cm×2.5cm×1.5cm = 15cm³
Now, Volume of 12 such matchboxes will be 12×15cm³ = 180cm³
Therefore, the volume of a packet containing 12 such matchboxes will be 180cm³.
Question 2. A cuboidal water tank is 6m long, 5m wide and 4.5m deep. How many litres of water can it hold? (1 m³= 1000 l)
Solution:
Given,
Dimensions of the cuboidal water tank
l = 6m, b = 5m, h = 4.5m
As we know, Volume of a cuboid = l×b×h
So, Volume of the tank = 6m×5m×4.5m = 135m³
We are given that, amount of water that 1m³ volume can hold = 1000 l
Amount of water, 135 m³volume hold = (135×1000) litres = 135000 litres
Therefore, given cuboidal water tank can hold up to 135000 litres (135 Kilo Litres) of water.
Question 3. A cuboidal vessel is 10m long and 8m wide. How high must it be made to hold 380 cubic meters of a liquid?
Solution:
Given,
Dimensions of cuboidal vessel
l = 10m, b = 8m, h = ?
Let height be h,
Volume of the vessel = 380m³
We know Formula for cuboid = l×b×h
10×8×h = 380
h = 4.75m
Therefore, height of vessel is 4.75m
Question 4. Find the cost of digging a cuboidal pit 8m long, 6m broad, and 3m deep at the rate of Rs 30 per m³?
Solution:
Given,
Dimensions of cuboidal pit
l = 8m, b = 6m, h = 3m
We know volume of a cuboid=l×b×h
So, volume of cuboidal pit = 8×6×3=144m³
Now, Cost of digging per m³ volume = Rs 30
Therefore, Cost of digging 144 m³ volume = Rs (144×30) = Rs 4320
Question 5. The capacity of a 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 m.
Solution:
Given,
Dimensions of cuboidal tank
l = 2.5m, b = ?, h = 10m
We know, Volume of cuboid = l×b×h
Volume of tank = 2.5×b×10 = 25bm³
As 1m³ = 1000Litres, Capacity of the tank = 25b×1000 = 25000bLitres
Also, capacity of a cuboidal tank is 50000 litres of water (Given)
Therefore, 25000 b = 50000
So, b = 2
Therefore, the breadth of the tank is 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?
Solution:
Given,
Dimensions of tank
l = 20 m, b = 15 m, h = 6 m
Total population of the village = 4000
Consumption of the water per head per day = 150 litres
Water consumed by the people in one day (4000×150) litres = 600000 litres.
Volume of cuboid = l×b×h
Volume of the tank will be 20×15×6=1800m³
Capacity of the tank=1800×1000litres=1800000litres
Let water in this tank last for d days.
Water consumed by all people in d days = Capacity of tank.
600000 d =1800000
d = 3
Therefore, the water of this tank will last for 3 days.
Question 7. A godown measures 40 m×25m×15 m. Find the maximum number of wooden crates each measuring 1.5m×1.25 m×0.5 m that can be stored in the godown.
Solution:
Given,
Dimensions of godown
l = 40m, b = 25m, h = 15m
Dimensions of wooden crate
l = 1.5m, b = 1.25m, h = 0.5m
Since godown and wooden crate are in cuboidal shape. Find the volume by, V = l×b×h.
Now, Volume of godown = (40×25×15) m³ = 15000 m³
And, Volume of a wooden crate = (1.5×1.25×0.5) m³ = 0.9375 m³
Let us consider that, n wooden crates can be stored in the godown, then
The volume of n wooden crates = Volume of godown
0.9375 × n =15000
n= 15000/0.9375 = 16000
Therefore, the number of wooden crates that can be stored in the godown is 16,000
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:
Given, side of cube = 12cm
We know volume of cube = (side)³ = (12)³ = 1728m³
Surface area of cube = 6a² = 6(12)²…eq(1)
Cube is cut into eight small cubes of equal volume, say side of each cube is c.
Volume of a small cube = c³
Surface area of a small cube = 6c² …eq(2)
Volume of each small cube = (1728/8) cm³ = 216 cm³
Or (c)3 = 216 cm³
Or c = 6 cm
Now, Surface areas of the cubes ratios = (Surface area of bigger cube)/(Surface area of smaller cubes)
From eq (1) and (2), we get
Surface areas of the cubes ratios = (6a²)/(6c²) = a²/c² = 122/62 = 4
Therefore, the required ratio is 4 : 1.
Question 9. A river 3m deep and 40m wide is flowing at the rate of 2km per hour. How much water will fall into the sea in a minute?
Solution:
Given,
Depth of river, h = 3 m
Width of river, b = 40 m
Rate of water flow = 2km per hour = 2000m/60min = 100/3 m/min
Now, Volume of water flowed in 1 min = (100/3) × 40 × 3 = 4000m³
Therefore, 4000 m³ water will fall into sea in a minute.