问题14.电影院大厅的尺寸为100 m,50 m,18 m。如果每个人需要150 m 3的空气,可以在大厅里坐多少人?
解决方案:
Length of hall = 100 m
Breadth of hall = 50 m
Height of hall = 18 m
So, the Volume of the hall = l × b × h
= 100 × 50 × 18 = 90000 m3
Also, the volume of air required per person = 150 m3
So we can say the number of persons who can sit in the hall will be given by, Volume of Hall/Volume of air required by one person
= 90000/150 = 600 persons
Hence, 600 persons can sit in the hall, if each person requires 150 m3 of air
问题15.假设1立方厘米的大理石重0.25千克,则大理石块的重量为28厘米,5厘米厚,为112千克。找到块的长度。
解决方案:
Given,
Breadth of marble block = 28 cm
Height of marble block = 5 cm
Let l be the length of the block
So, the Volume of the block = l × b × h
= l × 28 × 5 = 140l cm3
Since weight of 1cm3 is 0.25 kg
So, weight of marble block will be 0.25 × 140l kg
The total weight of marble is 112 kg
So, we can say
112 = 0.25 × 140l
l = 3.2 cm
Hence, the length of marble block is 3.2 cm
问题16.一个带盖的盒子是由2厘米厚的木头制成的。它的外部长度,宽度和高度分别为25厘米,18厘米和15厘米。可以在其中放入多少立方厘米的流体?另外,找到其中使用的木材的体积。
解决方案:
Given,
External length of box = 25 cm
External breadth of box = 18 cm
External height of box = 15 cm
So, the volume of the external box = l × b × h
= 25 × 18 × 15 = 6750 cm3
Now, the internal dimensions of the box will be given as,
The length will be 25 -(2 × 2) = 21 cm
The breadth will be 18 -(2 × 2) = 14 cm
The height will be 15 -(2 × 2) = 11 cm
Now, the internal volume of the cuboid is given as l × b × h
= 21 × 14 × 11 = 3234 cm3
So, we can say the volume of liquid that can be filled in the cuboid box = 3234 cm3
And the volume of wood needed or used = External volume of the box -Internal volume of the box
= 6750 -3234 = 3516 cm3
Hence, the volume of liquid that can be filled inside the box is 3234 cm3 and the volume of wood needed or used is 3516 cm3
问题17:封闭的木箱的外部尺寸为48厘米,36厘米,30厘米。盒子是用1.5厘米厚的木头制成的。这个盒子可以放多少块6厘米×3厘米×0.75厘米的砖?
解决方案:
Given,
External length of wooden box = 48 cm
External breadth of wooden box = 36 cm
External height of wooden box = 30 cm
Also, the thickness of wood is 1.5 cm
So, the internal dimensions of the box can be given as,
The length will be 48 -(2 × 1.5) = 45 cm
The breadth will be 36 -(2 × 1.5) = 33 cm
The height will be 30 -(2 × 1.5) = 27 cm
Now, the internal volume of the cuboid is given as l × b × h
= 45 × 33 × 27 = 40095 cm3
The dimensions of brick are given as 6 cm × 3 cm × 0.75 cm
So, the volume of brick will be l × b × h
= 6 × 3 × 0.75 = 13.5 cm3
Therefore, we can say the number of bricks that can be put inside the wooden box = Internal volume of the wooden box/Volume of one brick
= 40095/13.5 = 2970 bricks
Hence, the number of bricks that can be put inside the wooden box is 2970.
问题18.一个敞开的盒子中有多少立方厘米的铁,其外部尺寸分别为36 cm,25 cm和16.5 cm,整个铁的厚度为1.5 cm?如果1立方厘米的铁重15克。找到空盒的重量(以千克为单位)。
解决方案:
The external length of iron = 36 cm
The external breadth of iron = 25 cm
The external height of iron = 16.5 cm
So, the external volume is given as = l × b × h
= 36 × 25 × 16.5 = 14850 cm3
Also, the internal dimensions of the iron can be given as,
The length will be 36 -(2 × 1.5) = 33 cm
The breadth will be 25 -(2 × 1.5) = 22 cm
The height will be 16.5 -1.5 = 15 cm
Now, the internal volume of the cuboid is given as l × b × h
= 33 × 22 × 15 = 10890 cm3
Therefore, the weight of iron = External volume -Internal volume
= 14850 -10890 = 3960 cm3
And the weight of iron is given as, 15 × 3960 = 59400 gm = 59.4 kg
Hence, the weight of iron is 59.4 kg
问题19:将一个9厘米长的立方体完全浸入装有水的矩形容器中。如果底座的尺寸分别为15厘米和12厘米,请找到容器中水位的升高。
解决方案:
Given, the edge of cube = 9 cm
So, we can say the volume of a cube = (edge)3
= 93 = 729 cm3
The dimensions of the base of the rectangular vessel are 15 cm × 12 cm
So, the area of rectangular base = l × b
= 15 × 12 = 180 cm2
Now, the rise in water level in the vessel will be given as,
Volume of cube/Area of base of rectangular vessel = 729/180 = 4.05 cm
Hence, the rise of water level in the vessel is about 4.05 cm
问题20:一个矩形容器,其底部为一个边长为5cm的正方形,它站立在水平桌上,并盛放距顶部不超过1cm的水。当将固体立方体放入水中时,它会完全浸没,水会升至顶部,并溢出2立方厘米的水。计算立方体的体积以及其边缘的长度。
解决方案:
Let a be the edge of each cube
From the Questiontion, we can conclude that the volume of the cube will be equal to the sum of the volume of water present inside the tank and the volume of water that overflowed from the tank
So, the volume of cube = The volume of water present inside the tank + The volume of water that overflowed from the tank
a3 = (5 × 5 × 1) + 2
a3 = 27
a = 3 cm
So, the volume of the cube is 27 cm3
And edge will be 3 cm
Hence, the volume and edge of the cube are 27 cm3 and 3 cm respectively.
问题21.一个田地长200 m,宽150 m。在田野附近有一块地块,长50 m,宽40 m。该地块挖深7m,取出的土地均匀分布在田野上。场的高度提高了多少米?给出答案的小数点第二位。
解决方案:
The dimensions of earth dug out = 50 m × 40 m × 7 m
So, the volume of earth dug out = l × b × h
= 50 × 40 × 7 = 14000 m3
Let the height of the field rise by h m
Also, we know that volume of the field will be equal to the volume of earth dug out
So, 200 × 150 × h = 14000
h = 0.47 m
Hence, the level of the field raised by 0.47 m
问题22.一个字段的形式为矩形长度为18m,宽度为15m。在田间的一个角落挖了一个长7.5m,宽6m ,深0.8m的坑,取出的土地散布在田间的其余区域。找出提高该领域水平的程度。
解决方案:
Let the height of the field rise by h m
The volume of earth taken out of the pit will be, l × b × h
= 7.5 × 6 × 0.8 = 36 m3
Also, the earth is spread out on the field whose area can be given by 18 × 15 -7.5 × 6
= 225 m2
As we also know, the volume of earth taken out from pit = Area of the field × h
So, 36 = 225 × h
h = 16 cm
Hence, the level of the field has been raised by 16 cm
问题23:一个矩形水箱长80 m,宽25 m。水通过横截面为25 cm 2的管道以每小时16 km的速度流入管道。 45分钟内水箱中的水位上升了多少?
解决方案:
Let h cm be the rise in water level
So, the volume of the water tank is given as l × b × h
= 8000 × 2500 × h cm3
Also, the cross-sectional area of the pipe is 25 cm2
From the Questiontion, we can say the water coming out of the pipe forms a cuboid of base area 25 cm2, and length will be equal to the distance travelled with 16 kph in 45 minutes.
So, length = 16000 × 100 × 45/60 cm
So, we conclude the volume of water coming out of the pipe in 45 minutes = 25 × 16000 × 100 × 45/60
Also, the volume of water in the tank will be equal to the volume of water coming out of the pipe
Therefore, 8000 × 2500 × h = 25 × 16000 × 100 × 45/60
h = 1.5 cm
Hence, the level of water rises by 1.5 cm in the tank in 45 minutes.
问题24.一个底部为80 m x 60 m的矩形水库中的水深为6.5 m。如果水以15 km / hr的速度流过该管,横截面为边长20 cm的正方形的水可以在什么时候泵出。
解决方案:
Given, the flow of water in the pipe is 15km/hr
= 15000 m/hr
The volume of water coming out of the pipe in an hour can be given by,
20/100 × 20/100 × 15000 = 600 m3
Now the volume of the tank = l × b × h
= 80 × 60 × 6.5 = 31200 m3
Therefore, the time taken to fill the empty tank = Volume of tank/Volume of coming out of the pipe in an hour
= 31200/600 = 52 hours
Hence, the water must be pumped for 52 hours
问题25.一个人口为4000的村庄每天每人需要150升水。它有一个20 m×15 m×6 m的水箱。该水箱的水可持续使用几天?
解决方案:
Given, the length of the tank = 20 m
The length of tank = 15 m
The length of tank = 6 m
So, the volume/capacity of tank = l × b × h
= 20 × 15 × 6 = 1800 m3
= 1800000 litres
The amount of water consumed by people in the village = 150 × 4000 litres = 600000 litres
Let the water in the tank last for a days
So, the amount of water consumed by all people of the village in a days = Volume of tank
So, a × 600000 = 1800000
a = 3 days
Hence, the water will last for 3 days
问题26.一个孩子在玩积木,它是立方体的形状,已经建造了一个结构。如果每个立方体的边缘为3厘米,请找到孩子建造的结构的体积。
解决方案:
Volume of cube = edge3
= 33 = 27 cm3
Total number of the cube in the figure = 15
So, the volume of figure = 15 × 27 = 405 cm3
问题27.货仓尺寸为40 m×25 m×10 m。找到每个可存储在仓库中的最大木板箱数量,每个木板箱的尺寸为1.5 m×1.25 m×0.5 m。
解决方案:
Given, the dimensions of the godown are,
40 m × 25 m × 10 m
So, the volume of godown = l × b × h
= 40 × 25 × 10 = 10000 m3
Also, the dimensions of the wooden crate are,
1.5 m × 1.25 m × 0.5 m
So, the volume of the wooden crate = l × b × h
= 1.5 × 1.25 × 05 = 0.9375 m3
The number of wooden crates that can be stored = Volume of godown/Volume of one wooden crate
= 10000/0.9375 = 10666.66 wooden crates
Hence, approx 10667 wooden crates can be stored in the godown.
问题28.要在空旷的地面上建造一堵长10 m的墙。墙壁的高度为4 m,墙壁的厚度为24 cm。如果要用尺寸为24厘米×12厘米×8厘米的砖砌墙,则需要多少块砖?
解决方案:
Given, the dimensions of the wall are,
1000 cm × 24 cm × 400 cm
So, the volume of the wall = l × b × h
= 1000 × 24 × 400 = 9600000 cm3
Also, the dimensions of the brick are,
24 cm × 12 cm × 8 cm
So, the volume of the one brick = l × b × h
= 24 × 12 × 8 = 2304 cm3
The number of bricks required = Volume of wall/Volume of one brick
= 9600000/2304 = 4166.66 bricks
Hence, approx 4167 bricks are required to build the given wall.