8类RD Sharma解决方案-第21章，确定II(长方体和立方体的体积和表面积)-练习21.2 |套装1

问题1.找到尺寸为：的每个长方体的立方米(cu.m)的体积：
(i)长度= 12 m，宽度= 10 m，高度= 4.5 m
(ii)长度= 4 m，宽度= 2.5 m，高度= 50 cm
(iii)长度= 10 m，宽度= 25 dm，高度= 25厘米

解决方案：

i) length = 12 m, breadth = 10 m, height = 4.5 m

Since, Length (l) = 12 m

Breadth (b) = 10 m

Height (h) = 4.5 m

As we know, Volume of Cuboid = l × b × h

= 12 × 10 × 4.5 m³ = 540 m³

Hence, Volume of given cuboid is 540 m³

ii) length = 4 m, breadth = 2.5 m, height = 50 cm 

Since, Length (l) = 4 m

Breadth (b) = 2.5 m

Height (h) = 50 cm = 0.5 m

As we know, Volume of Cuboid = l × b × h

= 4 × 2.5 × 0.5 m³ = 5 m³

Hence, Volume of given cuboid is 5 m³

iii) length = 10 m, breadth = 25 dm, height = 25 cm

Since, Length (l) = 10 m

Breadth (b) = 25 dm = 2.5 m

Height (h) = 50 cm = 25 cm = 0.25 m 

As we know, Volume of Cuboid = l × b × h

= 10 × 2.5 × 0.25 m³ = 6.25 m³

Hence, Volume of given cuboid is 6.25 m³

问题2.求出边长为1的每个立方体的立方分米的体积
(i)1.5 m
(它)75厘米
(iii)2 dm 5厘米

解决方案：

i) 1.5 m

Since the side of cube = 1.5 m

As we know, Volume of Cube = (side)³

= (1.5)³ = 3.375 m³

As 1 m³ = 1000 dm³)

3.375 m³ = 3375dm³

Hence, Volume of the given cube is 3375 dm³

ii) 75 cm

Since the side of cube = 75 cm = 7.5 dm

As we know, Volume of Cube = (side)³

= (7.5)³ = 421.875 dm³

Hence, Volume of the given cube is 421.875 dm³

iii) 2 dm 5 cm

Since the side of cube = 2 dm 5 cm = 2.5 dm

As we know, Volume of Cube = (side)³

= (2.5)³ = 15.625 dm³

Hence, Volume of the given cube is 15.625 dm³

问题3.在挖一个3 m x 2 m x 5 m的井时挖出多少粘土?

解决方案：

Given, length of well = 3 m

The breadth of well = 2 m

The height of well = 5 m

Amount of clay dig out = Volume of well 

The volume of well = l × b × h = 3 × 2 × 5 m³

= 30 m³

Hence, the amount of clay dug out is 30 m³

问题4.如果体积为168 m ³的长方体的底部面积为28 m ² ，其高度将是多少?

解决方案：

Volume of cuboid = l × b × h = 168 m³

Area of cuboid = l × b = 28 m²

So, the height of the cuboid can be derived = Volume of cuboid/ Area of cuboid 

h = 168/28 m = 6 m

Hence, the height of the cuboid is 6 m

问题5.一个水箱长8 m，宽6 m ，高2 m。它可以容纳多少水?

解决方案：

Given, length of tank = 8 m

The breadth of tank = 6 m

The height of the tank = 2 m

Amount of water the tank can hold = Volume of tank 

The volume of tank = l × b × h = 8 × 6 × 2 m³

= 96 m³

(As 1 m³ = 1000 liters)

Hence, the amount of water the tank can hold is 96000 liters

问题6.某个立方形水箱的容量为50000升水。如果水箱的高度和长度分别为10 m和2.5 m，则求出水箱的宽度。

解决方案：

Given, volume of cuboidal tank = 50000 litres

The height of tank = 10 m

The length of tank = 2.5 m

We need to find breadth of the tank.

As 1 l = 1/1000 m³

So, 50000 l = 50 m³

Volume of cuboidal tank = l × b × h 

50 = 2.5 × b × 10 

b = 2 m 

Hence, the breadth of cuboidal tank is 2 m

问题7.矩形柴油油轮长2 m，宽2 m，深40 cm。它可以容纳多少升柴油?

解决方案：

Given, length of tanker = 2 m

The breadth of tanker = 2 m

The depth or height of tanker = 40 cm = 0.4 m

Amount of diesel tanker can hold = Volume of cuboidal tanker 

= l × b × h = 2 × 2 × 0.4 = 1.6 m³

And, 1.6 m³ = 1.6 × 1000 = 1600 litres

Hence, the tanker can hold 1600 litres of diesel

问题8.房间的长度，宽度和高度分别为5 m，4.5 m和3 m。查找其中包含的空气量。

解决方案：

Given, the length of room = 5 m

The breadth of room = 4.5 m

The height of room = 3 m

Volume of air the room can hold = Volume of Cuboidal room

= l × b × h = 5 × 4.5 × 3 = 67.5 m³

Hence, the volume of air the room can contain is 67.5 m³

问题9.一个水箱长3 m，宽2 m，深1 m。它可以容纳多少升水?

解决方案：

Given, the length of water tank = 3 m

The breadth of water tank = 2 m

The height of water tank = 1 m

Amount of water the tank can hold = Volume of Cuboidal water tank

= l × b × h = 3 × 2 × 1 = 6 m³

And, 6 m³ = 6000 litres

Hence, the water tank can hold 6000 litres of water.

问题10.用6 m长，75 cm宽，45 cm厚的木块可以制备多少块木板，每个木板长3 m，宽15 cm，厚5 cm?

解决方案：

Given, length of wooden block = 6 m

The breadth of wooden block = 75 cm = 0.75 m

The thickness/height of wooden block = 45 cm = 0.45 m

So, the volume of wooden block = l × b × h = 6 × 0.75 × 0.45

= 2.025 m³

Now, length of plank = 3 m

The breadth of plank = 15 cm = 0.15 m

The thickness/height of plank = 5 cm = 0.05 m

So, the volume of plank = l × b × h = 3 × 0.15 × 0.05

= 0.0225 m³

So, the number of plank that can be prepared from wooden block = volume of wooden block/ volume of plank 

= 2.025/0.0225 = 90 

Hence, 90 planks can be made from the given wooden block