6th Grade Math Textbook, Fundamentals

(Marvins-Underground-K-12) #1
Lesson 11-5 for exercise sets. &KDSWHU 

3UDFWLFH   $FWLYLWLHV

Find the surface area of the cylinder with given dimensions. Use ≈3.14.


1.h12 m; r4 m 2.h12 ft; r12 ft 3.h3.1 in.; r2 in.

Find the surface area of the cone with given dimensions. Use ≈3.14.


4.14 mm; r3 mm 5.100 yd; r10 yd 6.9.9 cm; r7 cm

7.Discuss and Write If you used the height of a cone instead of the slant
height to find its surface area, would your result be greater or less than
the actual surface area? Explain.

r  radius
5 yd

Base

Lateral
surface

  slant height
17.2 yd

r

 (^) 
r  5 yd
  17.2 yd
Base
Lateral
surface
Key Concept
Surface Area (S) of a Cone
Sr^2 rwhere Ssurface area,
rradius of the circular base, and
the slant height of the cone.


You can also find the surface area of a cone.

Find the approximate surface area of this cone.

The is the sum of the lateral area
and the area of its circular base. Like a cylinder, the
is the area of its lateral surface.
Unlike a cylinder, the lateral surface of a cone is not a
rectangle. The is the altitude of the
lateral surface.

When the cone is completely open, you have a piece of
a larger circle. Look at the diagram at the right. The two
red curves have exactly the same length.

Since you know the circumference of the base
of the cone is 2r, the ratio of the circumference
of the cone to the red arc of the circle is , or.
Multiplying this ratio by the area of the circle gives
the area of the lateral surface of the cone.


  • ^2 r


The area of the lateral surface of a cone is r.
The area of the circular base is r^2.
The total surface area isr^2 r.

So, using 3.14, the approximate surface area of the cone above is:

Area of the base: Ar^2
(5)^2  25 78.5 yd^2

Lateral area (LA): LAr
(5)(17.2)  86 270.04 yd^2

Total surface area (S): S 25  86  111 
or
S78.5 270.04 348.54 yd^2

So the area of the cone is approximately 348.54 square yards.

slant height of a cone

lateral area of a cone

surface area of a cone

r


2 r
2 

r

Free download pdf