6th Grade Math Textbook, Fundamentals

Lesson 11-9 for exercise sets. &KDSWHU 

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Find the volume of the cylinder or cone in terms of .

1.Cone: r 19 in.; h12 in. 2.Cylinder: r 1.4 km; h19.6 km

Find the unknown dimension. Use 3.14 for . Round to the nearest tenth.

3.Cylinder: V 930.4 m^3 ;r 5.25 m; h? 4.Cone: V 2034.72 cm^3 ;r ?; h24 cm

5.Discuss and Write Use two identical 8 11 sheets of paper. Roll and tape one vertically

and one horizontally to form two cylinders. Measure the dimensions and compute the

volume of each. Which has the greater volume? Explain why.

1

2

The volume of a cone is related to a cylinder’s volume in the same

way a pyramid’s volume is related to a prism’s volume. If a cone

and a cylinder have congruent bases and equal heights, the volume

of the cone is that of the cylinder.^13

Key Concept

V Bhor Vr^2 h, where Barea of the base,

rradius of the base, and hheight of the cone.

1

3

1

3

Volume (V) of a Cone

r

h

Find the volume, to the nearest hundredth, of the cone below.

Use 3.14 for .

V  Bh

 (r^2 )h

 (3.14 • 2^2 )4 Substitute known values.

 (12.56)4 Simplify within the parentheses.

 (50.24) 16.75

The cone has a volume of approximately 16.75 m^3.

If you know the volume of a cylinder or cone, you can use a formula and

algebra to solve for the length of a radius or an unknown height.

A cylindrical grain silo needs to hold

3956 yd^3 of grain and have a radius of

6 yd. How tall must the silo be in order

to hold the required amount of grain?

Use 3.14 for and round your answer

to the nearest yard.

So the grain silo must be at least 35 yd tall.

Substitute the formula for the area

of a circle forB.

1

3

1

3

1

3

1

3

1

3

P P

r

h

Vr^2 h

3956 (3.14 • 6^2 )h Use 3.14 for .

3956 (113.04)h



35 h

113.04h

113.04

3956

113.04