So, if you want to measure an irregular object's volume, just follow in Archimedes' footsteps (though you can omit the naked race part): Legend says that Archimedes was so excited about this discovery that he popped out of his bathtub and ran naked through the streets of Syracuse. Knowing the irregular object's volume and its weight, he could calculate the density and compare it with the density of pure gold. From this observation, he deduced that volume of water displaced must be equal to the volume of the part of his body he had submerged.
The idea came to him when he was taking a bath - stepping into a bathtub, he noticed that the water level rose. If it's an irregular shape, you can try to do the very thing that caused Archimedes to shout the famous word Eureka! Probably you heard that story - Archimedes was asked to find out if the Hiero's crown is made from pure gold or just gold-plated - but without bending or destroying it. For a right triangular prism, the equation can be easily derived, as well as for a right rectangular prism, which is apparently the same shape as a box.įor regular three-dimensional objects, you can easily calculate the volume by taking measurements of its dimensions and applying the appropriate volume equation. Prism = A h Ah A h, where A A A is a base area and h h h is the height. For a pyramid with a regular base, another equation may be used as well: Pyramid = ( n / 12 ) h s 2 cot ( π / n ) (n/12) h s^2 \cot(\pi/n) ( n /12 ) h s 2 cot ( π / n ), where n n n is a number of sides s s s of the base for a regular polygon. Pyramid = ( 1 / 3 ) A h (1/3)Ah ( 1/3 ) A h where A A A is a base area and h h h is the height.
Rectangular solid (volume of a box) = l w h lwh lw h, where l l l is the length, w w w is the width and h h h is the height (a simple pool may serve as an example of such shape). Sphere = ( 4 / 3 ) π r 3 (4/3)\pi r^3 ( 4/3 ) π r 3, where r r r is the radius.Ĭylinder = π r 2 h \pi r^2h π r 2 h, where r r r is the radius and h h h is the height.Ĭone = ( 1 / 3 ) π r 2 h (1/3)\pi r^2h ( 1/3 ) π r 2 h, where r r r is the radius and h h h is the height. Here are the formulas for some of the most common shapes:Ĭube = s 3 s^3 s 3, where s s s is the length of the side. You can also use our volume converter to convert your result to another unit of measure.There is no simple answer to this question, as it depends on the shape of the object in question. Use our length converter to convert your measurements to a consistent unit. If your measurements are in different units, convert each measurement to the unit you want the results in. One important consideration when measuring volume is to take all measurements using the same unit of measure. This technique is commonly used to estimate the volume of materials like gravel or water. The volume of a material is equal to the mass m divided by its density ρ. If you know the density of the material, you can calculate the volume using its mass with the following formula: In some cases, you can measure the volume of a fluid or irregular solid material by measuring its mass. Subtract the initial result by the result after the irregular object was placed in the water to find the volume of the object.Ī graduated cylinder is often used for finding the volume of small irregular shaped solids. Measure the amount of water as before and calculate the volume of the water with the object submerged. Submerge the irregular object in the water and observe that the water level in the container has risen.
The water displacement technique involves filling a container, that you know the volume of, with water and measuring the amount of water displaced by submerging the irregular object in the water in the container.įor example, fill a container with water and calculate the volume of the water using the formulas above. Water displacement is a technique used to find the amount of space an irregular object occupies. The formulas above can be used to calculate regular objects with a defined formula, but many objects are irregular or have no obvious formula.
Find volume of rectangular prism calculator how to#
How to Find the Volume of an Irregular Object
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