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In this lesson, we study some common space figures that are not polyhedra. Thesefigures have some things in common with polyhedra, but they all have some curved

surfaces, while the surfaces of a polyhedron are always flat.

First, the cylinder. The cylinder is somewhat like a prism. It has parallel congruentbases, but its bases are circles rather than polygons. You find the volume of a

cylinder in the same way that you find the volume of a prism: it is the product of the

base area times the height of the cylinder:

Since the base of a cylinder is always a circle, we can substitute the formula for the

area of a circle into the formula for the volume, like this:

Let's find the volume of this can of potato chips.

We'll use 3.14 for pi. Then we perform the calculations like this:

That's a lot of potato chips!

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A cone has a circular base and a vertex that is not on the base. Cones are similar in

some ways to pyramids. They both have just one base and they converge to a point,the vertex.

The formula for the volume of a cone is:

Since the base area is a circle, again we can substitute the area formula for a circle

into the volume formula, in place of the base area. The final formula for the volumeof a cone is:

Let's find the volume of this cone.

We can substitute the values into the volume formula. When we perform the

calculations, we find that the volume is 150.72 cubic centimeters.

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Finally, we'll examine the sphere, a space shape defined by all the points that are thesame distance from the center point. Like a circle, a sphere has a radius and a

diameter. The shape of the earth is like a large sphere -- it has radius of about 4000miles. A tennis ball is a sphere with a radius of about 2.5 inches.

Since a sphere is closely related to a circle, you won't be surprised to find that thenumber pi appears in the formula for its volume:

Let's find the volume of this large sphere, with a radius of 13 feet. Notice that the

radius is the only dimension we need in order to calculate the volume of a sphere.

If we substitute 13 feet for the radius, then we get 9,198.11 cubic feet.

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Match the descriptions below with an answer given in the list on the right bytyping its letter in the box provided. Round all answers to hundredths. Use

3.14 for pi.

Answers

Volume of a cone with height of 9 cm and radius of 7 cm

a. 267.95 cubic cm

Height of a cone with volume of 132 cubic cm and radius of 3 cm

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b. 1Volume of a cone with diameter 16 cm and height of 4 cm

c. 113.04 cubic ftVolume of a cylinder with radius of 5 cm and height of 3 cm

d. 461.58 cubic cmNumber of vertices on a cone

e. 0Number of vertices on a cylinder

f. 235.50 cubic cmVolume of a sphere with a radius of 3 ft

g. 14.01 cm

source : http://www.math.com/school/subject3/lessons/S3U4L4GL.html