7th Grade Math

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Surface Area

PART A BCDEF

Multi-Part

Lesson 2

Addresses

GLE 0706.1.3, GLE 0706.1.8.

598 Volume and Surface Area

Net of a Cone

HATS Corinne is making a party hat for her little

14 cm

6 cm

sister. It is in the shape of a cone and will be

covered with tissue paper. What is the surface area

of the cone that will be covered with tissue paper?

Construct a Net of a Cone

Use a compass to draw

14 cm

6 cm

two circles slightly

touching, one with a

radius of 6 centimeters

and one with a radius

of 14 centimeters.

Only a part of the larger circle is needed to make the

cone. Use a proportion to find the part.

circumference of

the smaller circle

portion that

is unknown

_37.70

87.96

= _x

360°

circumference of

the larger circle

total number of

degrees in a circle

Solve the proportion.

_37.70

87.96

= _x

360°

Write the proportion.

x(87.96) = 13,572 Cross multiply. 37.70 · 360 = 13,572

_x · 87.96

87.96^ =

_13,572

87.96

Divide each side by 87.96.

x ≈^154 Simplify.

You need 154° of the larger circle.

Cut a central angle of 154° from the larger circle and

make a cone.

154°

6 cm

14 cm

14 cm

6 cm

Main Idea

Justify the formula for

the surface area of a

cone by using a net.

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