问题11.假设建造中使用的沙子和水泥的量可以忽略不计,则建造几堵长5 m,高3 m和厚16 cm的墙需要多少块大小为25 cm x 10 cm x 8 cm的砖?
解决方案:
Given, length of brick = 25 cm
The breadth of brick = 10 cm
The height of brick = 8 cm
So, the volume of 1 brick = l × b × h
= 25 × 10 × 8 = 2000 cm3
2000 cm3 = 2000/1000000 m3 = 0.002 m3
Given, length of the wall = 5 m
The breadth of the wall = 16 cm = 0.16 m
The height of the wall = 3 m
So, the volume of wall = l × b × h= 5 × 0.16 × 3 = 2.4 m3
Number of bricks required = Volume of wall/ Volume of 1 brick
= 2.4/0.002 = 1200
Hence, 1200 bricks are required to build up the wall.
问题12:一个人口为4000的村庄每天每人需要150升水。它的水箱长20 m,宽15 m,高6 m。该水箱的水可持续使用几天?
解决方案:
Given, length of tank = 20 m
The width of tank = 15 m
The height of tank = 6 m
So, the volume of water tank = l × b × h = 20 × 15 × 6
= 1800 m3 Or 1800000 litres
Amount of water consumed by 1 villager = 150 litres
So, amount of water consumed by 4000 villagers = 150 × 4000 = 600000 litres
Number of days the water will end = Volume of water tank/ Amount of water consumed by villagers
= 1800000/ 600000 = 3 days
Hence, the water in tank will last till 3 days
问题13.一个矩形场长70 m,宽60 m。在田野外挖出尺寸为14 m×8 m×6 m的井,从该井挖出的泥土均匀地分布在田间。地平面会上升多少?
解决方案:
Given, length of well= 14 m
The width of well = 8 m
The height of well = 6 m
Volume of well = Volume of Earth dugout = l × b × h
= 14 × 8 × 6 = 672 m3
The length of rectangular field = 70 m
The width of rectangular field = 60 m
Let level of earth rise up by h m in the rectangular field
So, 70 × 60 × h = 672
= 0.16 m or 16 cm
Hence, the level of Earth rise up by 16 cm
问题14.一个游泳池长250 m,宽130 m。 3250立方米的水被抽入其中。找出水位的上升。
解决方案:
Given, length of pool = 250 m
The width of pool = 130 m
Volume of water in pool = 3250 m3
Let level of water rise up by h m
So, 250 × 130 × h = 3250
h = 0.1 m or 10 cm
Hence, the water level in pool rise up by 10 cm
问题15:5 m长,40 cm宽的横梁包含0.6立方米的木材。光束有多厚?
解决方案:
Given, length of beam = 5 m
The breadth of beam = 40 cm = 0.4m
Volume of wood in beam = 0.6m3
Let the thickness of beam is h m
So, 5 × 0.4 × h = 0.6
h = 0.3 m or 30 cm
Hence, the thickness of beam is 30 cm
问题16.某天的降雨量为6厘米。那天3公顷田地上掉了几升水?
解决方案:
Given, the area of field = 3 hectares
As 1 hectare = 10000 m2
So, area of field = 30000 m2
And the height of rain fall = 6 cm = 0.06 m
Amount of rain water fell on that day = Volume of rain water
= Area of field X height of rainfall = 30000 × 0.06 = 1800m3
Or 1800000 litres
Hence, 18 × 105 litres of rain water fell on the field
问题17:切成一块8 m长的立方形木梁可产生四千个1 cm的立方体,在此过程中不会浪费木材。如果光束的一个边缘为0.5 m,请找到第三条边缘。
解决方案:
Given, length of cuboidal beam = 8 m = 800 cm
The second edge of beam = 0.5 m = 50 cm
Number of small cubes so formed = 4000
Side of 1 cube = 1 cm
So, Volume of beam = Volume of small cubes = 4000 × Volume of 1 cube
= 4000 × (1 × 1 × 1) = 4000 cm3
So, we can state
Third edge of beam = Volume of beam/ (length of beam × second edge of beam)
= 4000/ 800 × 50 = 0.1 cm
Hence, the third edge of beam is 0.1 cm long
问题18.金属块的尺寸为2.25 m×1.5 m×27 cm。将其熔化并重铸成立方体,每边45厘米。形成了多少个立方体?
解决方案:
Given, length of block = 2.25 m
The width of block = 1.5 m
The height of block = 27 cm = 0.27 m
So, Volume of metal block = l × b × h = 2.25 × 1.5 × 0.27
= 0.91125 m3 = 911250 cm3
The side of cube = 45 cm
So, the volume of cube = (side)3
= 91125 cm3
Number of cubes that can be formed = Volume of metal block/ Volume of 1 cube
= 911250/91125 = 10
Hence, 10 cubes are formed from the metal block
问题19.一块实心的矩形铁块长6 m x 6 cm x 2 cm。如果1厘米3的铁重8克,求出这块的重量。
解决方案:
Given, length of rectangular piece = 6 m = 600 cm
The breadth of rectangular piece = 6 cm
The height of rectangular piece = 2 cm
So, Volume of rectangular piece = 600 × 6 × 2 = 7200 cm3
Since weight of 1 cm3 = 8 gm
So, weight of 7200 cm3 = 8 × 7200 = 57600 gm or 57.6 kg
Hence, the weight of iron piece is 57.6 kg
问题20.填写以下各项中的空白以使陈述正确:
(i)1 m 3 =………cm 3
(ii)1升=……。立方分米
(iii)1千升=……m 3
(iv)边长为8厘米的立方体的体积为……。 。
(v)长度为10厘米,宽度为8厘米的木制长方体的体积为4000 cm3。长方体的高度为……。厘米
(vi)1立方米dm =……。立方毫米
(vii)1立方公里=……立方米
(viii)1升=……。立方厘米
(ix)1毫升=………立方厘米
(x)1千升=………立方米=……。立方厘米
解决方案:
i) 1 m3 = 1000000 cm3
ii) 1 litre = 1 cubic decimetre
iii) 1 kl = 1 m3
iv) The volume of a cube of side 8 cm is 8 × 8 × 8 = 512 cm3
v) The volume of wooden cuboid of length 10 cm and breadth 8 cm is 4000 cm3. The height of the cuboid is
Volume/ length × breadth = 4000/ 10 × 8 = 50 cm
vi) 1 cu.dm = 1000000 cu.mm
vii) 1 cu.km = 1000000000 cu.m
viii) 1 litre = 1000 cu.cm
ix) 1 ml = 1 cu.cm
x) 1 kl = 1000 cu.dm = 1000000 cu.cm