问题1.火柴盒尺寸为4cm×2.5cm×1.5cm。包含12个这样的盒子的小包的容量是多少?
解决方案：
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.
问题2.一个长方体的水箱长6m，宽5m，深4.5m。它可以容纳多少升水? (1立方米= 1000升)
解决方案：
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.
问题3.立方形容器的长度为10m，宽度为8m。容纳380立方米液体必须达到多高?
解决方案：
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
问题4.是否找到以每立方米30卢比的价格开凿长8m，宽6m和深3m的长方体坑的成本?
解决方案：
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
问题5.立方形水箱的容量为50000升水。如果罐的长度和深度分别为2.5 m和10 m，则求出罐的宽度。
解决方案：
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.
问题6.一个人口为4000的村庄每天每人需要150升水。它的水箱尺寸为20 m×15 m×6 m。该水箱的水可持续使用几天?
解决方案：
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.
问题7：下水道尺寸为40 m×25m×15 m。找到每个可存储在仓库中的最大木板箱数量，每个木板箱尺寸为1.5m×1.25 m×0.5 m。
解决方案：
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
问题8.将一个边长为12厘米的实心立方体切成等体积的八个立方体。新立方体的一面是什么?另外，找到它们的表面积之间的比率。
解决方案：
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.
问题9：一条3m深，40m宽的河流以每小时2km的速度流动。一分钟内有多少水会掉入海中?
解决方案：
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.