Page 159 - NUMINO TG_6A
P. 159
Activity 2 Surface Areas of Cylinders
jOb ective Learn how to find the surface area of a cylinder using a net.
1. Textbook Instructions Activity 2 Surface Areas of Cylinders
Explain to students that the rectangle and Learn how to find the surface area of a cylinder using a net.
circles on the right are the three shapes, or
faces, that make up the cylinder shown on 3cm
the left. This type of representation is called a
net, and it gives us a way of visualizing three- 3cm 8cm
dimensional objects as two-dimensional 8cm
figures. The rectangle was the cylinder s
curved surface. One circle was the base, and Area of base A: 3 3 3.14 28.26 (cm2)
the other circle was the top. Nets also provide Length of lateral surface B: 3 2 3.14 18.84 (cm)
another way to find the surface area of a Area of lateral surface B: 18.84 8 150.72 (cm2)
three-dimensional object such as a cylinder. Surface area of the cylinder (2A + B): (28.26 2) + 150.72 = 207.24 (cm2)
1. Have students find the surface area using The length of the lateral surface is equal
the net of each cylinder.
to the circumference of the circle.
(length of lateral surface)
= (radius of circle) 2 π
Have students write down their answers Surface area of cylinder = (area of base) 2 + (area of lateral surface)
and explain how they calculated them.
Refer to . In order to find the surface area of a cylinder, students must add the area of the rectangle with two times
1 the area of the circle.
. Find the surface area using the net of each cylinder.
a. b. 2cm
4cm
4cm 6cm
(4 4 3.14) 2 (2 2 3.14) 2
+(4 2 3.14 4) 200.96 (cm2) +(2 2 3.14 6) 100.48 (cm2)
86
2. Build Understanding
Remind the students that they must add two times the area of the circle to the area of the rectangle to find
the surface area of a cylinder. Tell them that a cylinder has both a top and a base surface.
Example: 1a.
To find the area of the two circles, the radius (4 cm) is squared, multiplied by pi, and multiplied by 2. To
complete the problem, students must add the area of the bases to the area of the lateral surface. To find the
area of the lateral surface, they should multiply the radius (4 cm) by 2 (which calculates the diameter), by pi
(which determines the circumference), and by the height of the rectangle.
Remind them that the circumference of a circle is equal to the length of a rectangle.
Therefore, the surface area of the cylinder is: (4 4 3.14) 2 (4 2 3.14 4) 200.96 (cm2).
142 NUMINO Teacher s Guide
jOb ective Learn how to find the surface area of a cylinder using a net.
1. Textbook Instructions Activity 2 Surface Areas of Cylinders
Explain to students that the rectangle and Learn how to find the surface area of a cylinder using a net.
circles on the right are the three shapes, or
faces, that make up the cylinder shown on 3cm
the left. This type of representation is called a
net, and it gives us a way of visualizing three- 3cm 8cm
dimensional objects as two-dimensional 8cm
figures. The rectangle was the cylinder s
curved surface. One circle was the base, and Area of base A: 3 3 3.14 28.26 (cm2)
the other circle was the top. Nets also provide Length of lateral surface B: 3 2 3.14 18.84 (cm)
another way to find the surface area of a Area of lateral surface B: 18.84 8 150.72 (cm2)
three-dimensional object such as a cylinder. Surface area of the cylinder (2A + B): (28.26 2) + 150.72 = 207.24 (cm2)
1. Have students find the surface area using The length of the lateral surface is equal
the net of each cylinder.
to the circumference of the circle.
(length of lateral surface)
= (radius of circle) 2 π
Have students write down their answers Surface area of cylinder = (area of base) 2 + (area of lateral surface)
and explain how they calculated them.
Refer to . In order to find the surface area of a cylinder, students must add the area of the rectangle with two times
1 the area of the circle.
. Find the surface area using the net of each cylinder.
a. b. 2cm
4cm
4cm 6cm
(4 4 3.14) 2 (2 2 3.14) 2
+(4 2 3.14 4) 200.96 (cm2) +(2 2 3.14 6) 100.48 (cm2)
86
2. Build Understanding
Remind the students that they must add two times the area of the circle to the area of the rectangle to find
the surface area of a cylinder. Tell them that a cylinder has both a top and a base surface.
Example: 1a.
To find the area of the two circles, the radius (4 cm) is squared, multiplied by pi, and multiplied by 2. To
complete the problem, students must add the area of the bases to the area of the lateral surface. To find the
area of the lateral surface, they should multiply the radius (4 cm) by 2 (which calculates the diameter), by pi
(which determines the circumference), and by the height of the rectangle.
Remind them that the circumference of a circle is equal to the length of a rectangle.
Therefore, the surface area of the cylinder is: (4 4 3.14) 2 (4 2 3.14 4) 200.96 (cm2).
142 NUMINO Teacher s Guide
