Volume of Cylinder

Ever wondered what shape a Pringles container looks like? Or how much sugar would be needed to fill it if it were emptied of all Pringles? 

Volume of Cylinder Volume of Cylinder

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    Knowing what cylinders are and how to calculate their volume can easily aid you in measurements in reality because so many food items are stored in cylindrical containers.

    In this article, we will learn more about cylinders and how to calculate their volumes.

    What is a cylinder?

    A cylinder is a solid that has two identical circular flat ends connected with a tube.

    A cylinder is seen in many daily use objects such as toilet tissue, candy container, tin milk container, pipes, etc.

    Types of cylinders

    There are two basic types of cylinders.

    The right circular cylinders: These cylinders have the planes of their bases perpendicular to the segment connecting the centers of the cylinder's circles.

    Volume of Cylinders An image of a right circular cylinder StudySmarterAn image of a right circular cylinder, StudySmarter Originals

    The Oblique circular cylinder - These cylinders do not have the planes of their bases perpendicular to the segment connecting the centers of the cylinder's circles.

    Volume of Cylinders An image of an oblique circular cylinder StudySmarter An image of an oblique circular cylinder, StudySmarter Originals

    How to calculate the volume of a cylinder?

    Volume of a circular cylinder

    The volume of a circular cylinder is calculated by multiplying its height by the area of its circular base.

    We recall that the area of a circle is given by,

    Areacircle=πr2

    Thus, the volume of a circular cylinder is given by,

    Volume circular cylinder=Areacircular base×height=πr2×h

    A cylindrical container has a base radius of 7 cm and a depth of 10 cm. Find the volume if π=227

    Solution:

    We first note the radius and the height of the cylinder, r=7 cm, h= 10 cm.

    The volume of the circular cylinder is calculated as,

    Vcircular cylinder=πr2×h=227×72×10=220×7=1540 cm3

    Volume of an oblique circular cylinder

    Cavalieri's Principle

    Cavalieri's principle states that for any two solids having the same height and are such that their corresponding cross-sections at any level, have the same areas, then they have the same volume.

    Cavalieri's principle is very important in finding volumes of oblique solid shapes. It enables us to use the same formula in calculating the volumes of these solids even though they are not straight.

    According to Cavalieri's principle, considering two circular and oblique cylinders of the same height, having the same radius on their bases, we deduce that they will share the same cross-section areas. Hence, we can say that the volume of an oblique cylinder is equal to the volume of a right circular cylinder. Therefore the volume of an obliques cylinder, Vo is given by

    Voblique cylinder=Vcircular cylinder=πr2×h

    Find the volume of the figure below, taking π=227.

    Solution:

    Recalling Cavalier's principle,

    Voblique cylinder=Vcircular cylinder=πr2h

    We deduce from the figure thatr=9 cm, h=28 cm.

    Thus, the volume of the oblique cylinder given in the above figure can be calculated as,

    Voblique cylinder=227×92×28=22×81×4=7128 cm3.

    What unit is the volume of a cylinder measured in?

    The volume of a cylinder is measured in cubic centimeters cm3 and cubic meters m3 . Also, the volume of a cylinder is measured in liters l. Note that:

    1000cm3=1l1cm3=0.001l

    Volume of a semicircular cylinder

    A semicircular cylinder has its base and top as a semicircle. It is also known to be half of a right circular cylinder.

    Volume of Cylinders An image of a semicircular cylinder StudySmarter An image of a semicircular cylinder, StudySmarter Originals

    The volume of a semicircular cylinder is calculated by dividing the volume of the completed cylinder by 2.

    Imagine that the semicircular cylinder is completed to become a full cylinder. Thus,

    Volumefull formed cylinder=πr2×h

    Then the volume of a semicircular cylinder is given by,

    Vsemicircular cylinder=πr2×h2

    Find the volume of a semicircular cylinder with a height of 6 cm and a diameter of 5 cm. Take π=227.

    Solution:

    The volume of a semicircular cylinder is given by,

    Vsemicircular cylinder=πr2×h2

    We write down the height and the diameter from the given,h= 6 cm, d= 5 cm.

    We deduce the radius from the diameter, r=diameter 2=52 cm.

    Hence, the volume of the semicircular cylinder is given by,

    Vsemicircular cylinder=πr2×h2=π×522×62=227×254×62=3300282=58.93 cm3.

    How to calculate the volume of irregular shapes?

    Knowledge of the volume of regular solids makes the calculation of irregular shapes possible. Firstly, you have to break down the irregular solid to its regular solid components then you determine its volume.

    Let's see how this can be done in the following example.

    Determine the volume of the casket below. Take π=227.

    Solution:

    We first note that the top of the casket is a semicircular cylinder while the base is a rectangular prism.

    Let us find the volume of the semicircular cylindrical top.

    Vsemicircular cylinder=πr2×h2

    We note that the diameter of the semicircular cylinder is d=14 cm. Thus, r=diameter 2=d2=142=7 cm.

    Hence,

    Vsemicircular cylinder=πr2×h2=227×72×302=22×7×302=2310 cm3.

    The volume of the rectangular prism,

    Vrectangular prism=length ×breadth×height of the prism

    From the figure, we deduce that length = 30 cm, breadth = 14 cm and height = 15 cm.

    Hence,

    Vrectangular prism=30×14×15=6300 cm3.

    The volume of the casket is calculated as the sum of the volume of the semicircular cylinder and the volume of the rectangular prism.

    Vcasket=Vsemicircular cylinder+Vrectangular prism=2310+6300=8610 cm3.

    How many tissue rolls does Brenda need to block 40 425 cubic centimeters opening in her room if the height of the roll is 50 cm? Take π=227.

    Solution:

    To determine how many rolls of tissues Brenda has to use, we need to find the volume of the tissue, Vtissue.

    The volume of the tissue can be calculated by subtracting the volume of the tissue's hollow space, from the volume of the whole cylinder.

    Thus,

    Vtissue=Vwhole cylinder-Vhollow space

    We calculate first the volume of the whole cylinder,

    Vwhole cylinder=π×r2×h=π×2822×50=227×142×50=30 800 cm3

    Next, in order to calculate the volume of the hollow space, we first need to calculate its corresponding radius. But the diameter of the hollow space can be found by subtracting the diameter of the whole cylinder from the diameter of the non-empty cylinder, thus

    diameterhollow cylinder=28-7=21 cm

    Now, the volume of the hollow space is,

    Vhollow space=π×r2×h=227×2122×50=17 325 cm3.

    Thus the volume of the tissue is,

    Vtissue=Vwhole cylinder-Vhollow space=30 800- 17 325=13 475 cm3.

    Since the volume of the space Brenda is to fill is 40 425 cm3, then she would need,

    (40 425÷13 475)tissues=3 tissues.

    Volume of Cylinder - Key takeaways

    • A cylinder is a solid that has two identical circular flat ends connected with a tube.
    • The two types of cylinders are the right circular and oblique circular cylinders.
    • Cavalieri's principle states that for any two solids which possess the same height as well as cross-sectional area, their volumes are the same.
    • The volume of a cylinder is given by Vcylinder=π×r2×h.
    • A semicircular cylinder has its base and top as a semicircle. It is also known to be half of a right circular cylinder.
    Frequently Asked Questions about Volume of Cylinder

    Find the volume of a cylinder.

    The volume of a cylinder is calculated by multiplying the area of its circular base by the height of the cylinder.

    What is the formula for finding the volume of a cylinder ?

    The formula for finding the volume of a cylinder is; pie times the square of radius times the height.

    What is the volume of the right cylinder? 

    The volume of a right cylinder is calculated in the same way as calculating the volume of a cylinder.

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