Lesson Solved problems on volume of cones

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> Lesson Solved problems on volume of cones      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

This Lesson (Solved problems on volume of cones) was created by by ikleyn(52786) About Me : View Source, Show
About ikleyn:

Solved problems on volume of cones


In this lesson you will find typical solved problems on volume of cones.
The theoretical base for these problems is the lesson  Volume of cones  under the topic  Volume, metric volume  of the section  Geometry  in this site.


Problem 1

Find the volume of a cone if the base radius of the cone is of  4 cm  and the height of the cone is of  9 cm.

Solution

Apply the formula for the volume of a cone.  The volume is

V = 1%2F3pi.r%5E2h = 1%2F3pi.4%5E2.9 = 1%2F3pi.16%29.9 = 48%2Api = 150.8 cm%5E3 (approximately).

Answer.  The volume of the cone is  150.8 cm%5E3 (approximately).


Problem 2

Find the volume of a combposite solid body which comprises of two identical cones joined base to base  (Figure 3),  if their common base radius is of  4 cm  and the height
is of  3 cm  each.

Solution

We are given a 3D body comprised of two identical cones whose bases are joined and                          
overposed each to the other  (Figure 3).

The volume of each single cone is

V%5B1%5D = 1%2F3pir%5E2h = 1%2F3pi.4%5E2.3 = 16pi cm%5E3.

The volume of the given composite body is doubled this value, i.e.

V = 2%2AV%5B1%5D = 32pi = 3.14159*24 = 100.53 cm%5E3 (approximately).



Figure 3. To the Problem 2

Answer.  The volume of the given composite body is  100.53 cm%5E3 (approximately).


Problem 3

A composite solid body comprises of the cone and the cylinder that have the same base radius measure.  The cone and the cylinder are joined base to base in a way that the centers of their bases coincide  (Figure 4).  Find the volume of the given body if the common base radius is of  4 cm  and the height of the cone and the cylinder is of 3 cm.

Solution

We are given a 3D body comprised of the cone and the cylinder with identical base                              
radii measures whose bases are joined and overposed each to the other  (Figure 4).

The volume of the cone is

V%5Bcone%5D = 1%2F3pir%5E2h = 1%2F3pi.4%5E2.3 = 16%2Api = 50.265 cm%5E3 (approximately).

The volume of the cylinder is

V%5Bcylinder%5D = pir%5E2h = pi.4%5E2.3 = 48%2Api = 150.8 cm%5E3 (approximately).

The total volume of the composite solid body is the sum of these values

V = V%5Bcone%5D + V%5Bcylinder%5D = 1%2F3pir%5E2h + pir%5E2h = 50.266 + 150.8 = 201.06 cm%5E3 (approximately).



Figure 4. To the Problem 3

Answer.  The volume of the composite body is  201.06 cm%5E3 (approximately).


Problem 4

Find the volume of a body  (a truncated cone)  obtained from a cone with the base radius of  4 cm  and the height of  6 cm  after cutting off the part of the cone by the plane parallel to the base in a way that the cutting plane bisects the height of the original cone  (Figure 5).

Solution

The strategy solving this problem is to find first the volume of the entire cone with                            
the base radius of  6 cm  and the height of  8 cm  and then to distract the volume
of the cone with the base radius of  3 cm  and the height of  4 cm.

The volume of the original entire cone is   1%2F3pi%2Ar%5E2%2Ah,  where  r= 4 cm  is the cone base
radius and  h= 6 cm  is the cone height.  So, the volume of the cone is

V = 1%2F3pi%2A4%5E2%2A6 = 32%2Api cm%5E3.

The small cone has the base radius of  1%2F24 = 2 cm  and the height of  1%2F26 = 3 cm.
Therefore,  the volume of the small cone is  1%2F3pi%2A2%5E2%2A3 = 4%2Api cm%5E3.



    Figure 5. To the  Problem 4

Thus the volume of the truncated cone under consideration is  32%2Api - 4%2Api = 28%2Api = 3.14159*28 = 87.96 cm%5E3 (approximately).

Answer.  The volume of the truncated cone is  87.96 cm%5E3 (approximately).


My lessons on volume of cones and other 3D solid bodies in this site are

Lessons on volume of prisms

Volume of prisms
Solved problems on volume of prisms
Overview of lessons on volume of prisms                    

Lessons on volume of pyramids

Volume of pyramids
Solved problems on volume of pyramids
Overview of lessons on volume of pyramids

Lessons on volume of cylinders

Volume of cylinders
Solved problems on volume of cylinders
Overview of lessons on volume of cylinders                

Lessons on volume of cones

Volume of cones
Solved problems on volume of cones
Overview of lessons on volume of cones                    

Lessons on volume of spheres

Volume of spheres
Solved problems on volume of spheres
Overview of lessons on volume of spheres


To navigate over all topics/lessons of the Online Geometry Textbook use this file/link  GEOMETRY - YOUR ONLINE TEXTBOOK.

This lesson has been accessed 9467 times.