[\/et_pb_text][et_pb_text _builder_version=”4.11.3″ _module_preset=”default” text_font_size=”16px” header_2_text_color=”gcid-70a40ab1-38f4-4842-b1ac-1e69b0045607″ custom_padding=”|15px||4px|false|false” global_colors_info=”{%22gcid-70a40ab1-38f4-4842-b1ac-1e69b0045607%22:%91%22header_2_text_color%22%93}”]<\/p>\n
Volume: Meaning and formula.<\/strong><\/h2>\nVolume is the measure of the amount of space occupied or enclosed by any three-dimensional object by the surfaces in cubic units. As each of the measures are linear measurements, the units of volumes are derived from the units of length.<\/p>\n
Formula:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong><\/p>\nTo find out the volume of the 3D cuboidal object, we multiply its length(l), width(b), and height(h).<\/p>\n
In the mathematical expression:<\/p>\n
Volume = length \u00d7 width \u00d7 height<\/span><\/p>\nV = l \u00d7 b \u00d7 h<\/span><\/p>\nThus, we have three units of dimensions (length, width, and height), so the volume is measured in cubic units.<\/p>\n
Let\u2019s understand with an example:<\/p>\n
The length of a water tanker is 8 feet and height is 7 feet and the width of the tanker is 3 feet. Find the volume of the water tanker.<\/p>\n
By putting the values of the given dimensions in the formula.<\/p>\n
SI units of Volume<\/strong><\/h2>\nThe SI unit of volume is cubic meter (m3<\/sup>). However, there are also other units to measure small and large quantities of volume.<\/p>\nCommon Units of Volume in cubic meters<\/p>\n
\n\n\n\u00a0cubic kilometer<\/td>\n Km3<\/sup><\/td>\n1 x 10003<\/sup> m3<\/sup><\/td>\n1,000,000,000 m3<\/sup><\/td>\n<\/tr>\n\nhectometer<\/td>\n Hm3<\/sup><\/td>\n1 x 1003<\/sup> m3<\/sup><\/td>\n1,000,000 hm3<\/sup><\/td>\n<\/tr>\n\nDecameter cubic<\/td>\n dam3<\/sup><\/td>\n1 x 103 <\/sup>m3<\/sup><\/td>\n1000 m3<\/sup><\/td>\n<\/tr>\n\ncubic meter<\/td>\n m3<\/sup><\/td>\n1 m3<\/sup><\/td>\n1 m3<\/sup><\/td>\n<\/tr>\n\ncubic decimeter<\/td>\n dm\u00b3<\/td>\n 1 x 10-3<\/sup><\/td>\n0.001 m3<\/sup><\/td>\n<\/tr>\n\ncubic centimeter<\/td>\n cm\u00b3<\/td>\n 1 x 100-3<\/sup> m3<\/sup><\/td>\n0.000001 m3<\/sup><\/td>\n<\/tr>\n\nCubic millimeter<\/td>\n mm3<\/sup><\/td>\n1 x 1000-3<\/sup> m3<\/sup><\/td>\n0.000000001 m<\/td>\n<\/tr>\n<\/thead>\n<\/table>\n <\/p>\n
<\/p>\n
Note: Each unit is 1000 times more than the previous unit. To convert the one unit to other units accordingly either multiply or divide by the number of zeros that are there in place between the units. To convert a smaller unit into a greater unit we multiply the number of zeros between the units. And to convert a greater unit into a smaller unit we divide by the number of zeros between the units.<\/p>\n
Examples of everyday units:<\/p>\n
\n- 200 ml \u2013 Juice Box.<\/li>\n
- 500 ml \u2013 Cold drink bottle.<\/li>\n
- 15 ml \u2013 Eye drop.<\/li>\n
- 5l \u2013 Cooking Oil.<\/li>\n<\/ul>\n
Relationship between the Volume, Mass and Capacity<\/strong><\/h3>\nThere is a relationship that exists between capacity and volume. A liter (l) is the capacity equal to the volume of a cube that measures 10 cm3<\/sup> (1 dm3<\/sup>) on each side.<\/p>\nThere exists a direct relationship between the volume and mass of water. One gram equals to 1 cm3<\/sup> of pure water.<\/p>\n\n\n\nVolume<\/td>\n Capacity<\/td>\n Mass<\/td>\n<\/tr>\n \n1 m3<\/sup><\/td>\n1 kl<\/td>\n 1 t<\/td>\n<\/tr>\n \n1 dm3<\/sup><\/td>\n1 l<\/td>\n 1kg<\/td>\n<\/tr>\n \n1 cm3<\/sup><\/td>\n1 ml<\/td>\n 1g<\/td>\n<\/tr>\n<\/thead>\n<\/table>\n <\/p>\n
Example<\/strong><\/h3>\n\n- Convert into 1.76<\/span>hm<\/span>3<\/sup><\/span> into <\/span>m<\/span>3<\/sup><\/span><\/li>\n<\/ol>\n
Solution:<\/p>\n
1 hm3<\/sup>= 1 x 106 <\/sup>m3<\/sup><\/p>\nTo convert the hm3 <\/sup>into m3<\/sup>, multiply the volume by 106 <\/sup>(1,000,000) as there are two places between the units.<\/p>\n\n- Convert the 10 m3<\/sup> into liters.<\/li>\n<\/ol>\n
Solutions:<\/p>\n
We know 1 dm3<\/sup> is equal to 1 liter. In the above example, the value is given in the m3<\/sup>. So, we need to first convert the unit m3<\/sup> into dm3<\/sup> and then have a value in liters.<\/p>\n1<\/span>m<\/span>3<\/sup><\/span>=<\/span>1000dm<\/span>3<\/sup><\/span><\/p>\n10<\/span>m<\/span>3<\/sup><\/span>=10 \u00d7 1000<\/span>dm<\/span>3<\/sup><\/span>=100,000<\/span>dm<\/span>3<\/sup><\/span><\/p>\n\n- The height, width, and length of the rectangular tank are 6m, 7m, and 600 cm respectively. There is also another rectangular tank smaller in size with a volume of 20, 0000 dm3<\/sup>. Find out by how many cubic meters the volume of the bigger tank is more than the smaller tank.<\/li>\n<\/ol>\n
Solutions:<\/p>\n
Here, we have to find out the volume of the bigger rectangular tank with the given dimensions:<\/p>\n
Length of the tank = 600 cm = 6 m (1m = 100cm)<\/p>\n
Height of the tank = 6m.<\/p>\n
Width of the tank = 7m.<\/p>\n
The volume of the bigger tank:<\/p>\n
V = 6 \u00d7 7 \u00d7 6= 252<\/span>m<\/span>,<\/span><\/p>\nThe volume of the smaller tanker is given in cubic decimeters. First, we need to convert it into cubic meters.<\/span><\/p>\nThe volume of smaller tank = 20, 0000 dm<\/span>3<\/sup><\/span><\/p>\n1<\/span>m<\/span>3<\/sup><\/span>=<\/span>1000dm<\/span>3<\/sup><\/span><\/p>\nNote here, dm<\/span>3<\/sup><\/span> is a smaller unit than m<\/span>3<\/span>. Thus, we have to divide to convert the smaller unit into a bigger unit.<\/span><\/p>\n20,0000<\/span>dm<\/span>3<\/sup><\/span>=<\/span>20,0000<\/span>1000<\/span>m<\/span>3<\/sup><\/span>=200<\/span>m<\/span>3<\/sup><\/span><\/p>\nNow we have both the volumes in the same unit i.e. in cubic meters. We can find out the number of cubic meters by which the volume of the bigger rectangular tank exceeds the value of the smaller tank.<\/span><\/p>\n=<\/span>252m<\/span>3 <\/sup><\/span>– <\/span>200m<\/span>3<\/sup><\/span><\/p>\n=52<\/span>m<\/span>3<\/sup><\/span><\/p>\nThus, the volume of the bigger tank is 52m<\/span>3<\/sup><\/span> greater than the volume of the smaller tank.<\/span><\/p>\n [\/et_pb_text][et_pb_text admin_label=”Sample Questions
\n” _builder_version=”4.10.4″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”28px” custom_padding=”|0px||4px|false|false” global_colors_info=”{}”]<\/p>\n
Practice Multiple Choice Questions<\/h1>\n
[\/et_pb_text][et_pb_text admin_label=”Question 1″ _builder_version=”4.10.6″ _module_preset=”default” background_color=”#FFFFFF” custom_padding=”25px|25px|25px|25px|true|true” border_radii=”on|15px|15px|15px|15px” border_width_top=”3px” border_color_top=”#E02B20″ global_colors_info=”{}”]<\/p>\n
\n\nQuestion:
\n<\/b>PQRS is a rhombus. Each of its sides is 20 cm long, diagonal PR is 32 cm long and diagonal QS is 24 cm.<\/p>\n
![](\"http:\/\/www.educationalinitiatives.com\/detailed_assessment\/images\/DAM_50824.jpg\")
<\/p>\n
What is the area of PQRS?<\/p>\n
1. 384 cm\u00b2
\n2. 400 cm\u00b2
\n3. 560 cm\u00b2
\n4. 768 cm\u00b2<\/p>\n<\/div>\n
\nType your answer option :<\/b> <\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\nAnswer:<\/b> 1<\/span><\/span><\/div>\n
To find out the volume of the 3D cuboidal object, we multiply its length(l), width(b), and height(h).<\/p>\n
In the mathematical expression:<\/p>\n
Volume = length \u00d7 width \u00d7 height<\/span><\/p>\n V = l \u00d7 b \u00d7 h<\/span><\/p>\n Thus, we have three units of dimensions (length, width, and height), so the volume is measured in cubic units.<\/p>\n Let\u2019s understand with an example:<\/p>\n The length of a water tanker is 8 feet and height is 7 feet and the width of the tanker is 3 feet. Find the volume of the water tanker.<\/p>\n By putting the values of the given dimensions in the formula.<\/p>\n The SI unit of volume is cubic meter (m3<\/sup>). However, there are also other units to measure small and large quantities of volume.<\/p>\n Common Units of Volume in cubic meters<\/p>\n <\/p>\n <\/p>\n Note: Each unit is 1000 times more than the previous unit. To convert the one unit to other units accordingly either multiply or divide by the number of zeros that are there in place between the units. To convert a smaller unit into a greater unit we multiply the number of zeros between the units. And to convert a greater unit into a smaller unit we divide by the number of zeros between the units.<\/p>\n Examples of everyday units:<\/p>\n There is a relationship that exists between capacity and volume. A liter (l) is the capacity equal to the volume of a cube that measures 10 cm3<\/sup> (1 dm3<\/sup>) on each side.<\/p>\n There exists a direct relationship between the volume and mass of water. One gram equals to 1 cm3<\/sup> of pure water.<\/p>\n <\/p>\n Solution:<\/p>\n 1 hm3<\/sup>= 1 x 106 <\/sup>m3<\/sup><\/p>\n To convert the hm3 <\/sup>into m3<\/sup>, multiply the volume by 106 <\/sup>(1,000,000) as there are two places between the units.<\/p>\n Solutions:<\/p>\n We know 1 dm3<\/sup> is equal to 1 liter. In the above example, the value is given in the m3<\/sup>. So, we need to first convert the unit m3<\/sup> into dm3<\/sup> and then have a value in liters.<\/p>\n 1<\/span>m<\/span>3<\/sup><\/span>=<\/span>1000dm<\/span>3<\/sup><\/span><\/p>\n 10<\/span>m<\/span>3<\/sup><\/span>=10 \u00d7 1000<\/span>dm<\/span>3<\/sup><\/span>=100,000<\/span>dm<\/span>3<\/sup><\/span><\/p>\n Solutions:<\/p>\n Here, we have to find out the volume of the bigger rectangular tank with the given dimensions:<\/p>\n Length of the tank = 600 cm = 6 m (1m = 100cm)<\/p>\n Height of the tank = 6m.<\/p>\n Width of the tank = 7m.<\/p>\n The volume of the bigger tank:<\/p>\n V = 6 \u00d7 7 \u00d7 6= 252<\/span>m<\/span>,<\/span><\/p>\n The volume of the smaller tanker is given in cubic decimeters. First, we need to convert it into cubic meters.<\/span><\/p>\n The volume of smaller tank = 20, 0000 dm<\/span>3<\/sup><\/span><\/p>\n 1<\/span>m<\/span>3<\/sup><\/span>=<\/span>1000dm<\/span>3<\/sup><\/span><\/p>\n Note here, dm<\/span>3<\/sup><\/span> is a smaller unit than m<\/span>3<\/span>. Thus, we have to divide to convert the smaller unit into a bigger unit.<\/span><\/p>\n 20,0000<\/span>dm<\/span>3<\/sup><\/span>=<\/span>20,0000<\/span>1000<\/span>m<\/span>3<\/sup><\/span>=200<\/span>m<\/span>3<\/sup><\/span><\/p>\n Now we have both the volumes in the same unit i.e. in cubic meters. We can find out the number of cubic meters by which the volume of the bigger rectangular tank exceeds the value of the smaller tank.<\/span><\/p>\n =<\/span>252m<\/span>3 <\/sup><\/span>– <\/span>200m<\/span>3<\/sup><\/span><\/p>\n =52<\/span>m<\/span>3<\/sup><\/span><\/p>\n Thus, the volume of the bigger tank is 52m<\/span>3<\/sup><\/span> greater than the volume of the smaller tank.<\/span><\/p>\n [\/et_pb_text][et_pb_text admin_label=”Sample Questions [\/et_pb_text][et_pb_text admin_label=”Question 1″ _builder_version=”4.10.6″ _module_preset=”default” background_color=”#FFFFFF” custom_padding=”25px|25px|25px|25px|true|true” border_radii=”on|15px|15px|15px|15px” border_width_top=”3px” border_color_top=”#E02B20″ global_colors_info=”{}”]<\/p>\n Question: What is the area of PQRS?<\/p>\n 1. 384 cm\u00b2 Type your answer option :<\/b> <\/span><\/p>\nSI units of Volume<\/strong><\/h2>\n
\n\n
\n \u00a0cubic kilometer<\/td>\n Km3<\/sup><\/td>\n 1 x 10003<\/sup> m3<\/sup><\/td>\n 1,000,000,000 m3<\/sup><\/td>\n<\/tr>\n \n hectometer<\/td>\n Hm3<\/sup><\/td>\n 1 x 1003<\/sup> m3<\/sup><\/td>\n 1,000,000 hm3<\/sup><\/td>\n<\/tr>\n \n Decameter cubic<\/td>\n dam3<\/sup><\/td>\n 1 x 103 <\/sup>m3<\/sup><\/td>\n 1000 m3<\/sup><\/td>\n<\/tr>\n \n cubic meter<\/td>\n m3<\/sup><\/td>\n 1 m3<\/sup><\/td>\n 1 m3<\/sup><\/td>\n<\/tr>\n \n cubic decimeter<\/td>\n dm\u00b3<\/td>\n 1 x 10-3<\/sup><\/td>\n 0.001 m3<\/sup><\/td>\n<\/tr>\n \n cubic centimeter<\/td>\n cm\u00b3<\/td>\n 1 x 100-3<\/sup> m3<\/sup><\/td>\n 0.000001 m3<\/sup><\/td>\n<\/tr>\n \n Cubic millimeter<\/td>\n mm3<\/sup><\/td>\n 1 x 1000-3<\/sup> m3<\/sup><\/td>\n 0.000000001 m<\/td>\n<\/tr>\n<\/thead>\n<\/table>\n \n
Relationship between the Volume, Mass and Capacity<\/strong><\/h3>\n
\n\n
\n Volume<\/td>\n Capacity<\/td>\n Mass<\/td>\n<\/tr>\n \n 1 m3<\/sup><\/td>\n 1 kl<\/td>\n 1 t<\/td>\n<\/tr>\n \n 1 dm3<\/sup><\/td>\n 1 l<\/td>\n 1kg<\/td>\n<\/tr>\n \n 1 cm3<\/sup><\/td>\n 1 ml<\/td>\n 1g<\/td>\n<\/tr>\n<\/thead>\n<\/table>\n Example<\/strong><\/h3>\n
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\n” _builder_version=”4.10.4″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”28px” custom_padding=”|0px||4px|false|false” global_colors_info=”{}”]<\/p>\nPractice Multiple Choice Questions<\/h1>\n
\n<\/b>PQRS is a rhombus. Each of its sides is 20 cm long, diagonal PR is 32 cm long and diagonal QS is 24 cm.<\/p>\n<\/p>\n
\n2. 400 cm\u00b2
\n3. 560 cm\u00b2
\n4. 768 cm\u00b2<\/p>\n<\/div>\n