Page 158 - NUMINO Challenge_D2

The pairs of (Width, Length) that make an area 3 If you think that the plane figure is only on the
of 8 cm2 are (1, 8), (2, 4), (4, 2), and (8, 1). In this
case, since the width should be the shortest, left or right side of the rotation axis, then the
width=1 cm and length=8 cm. Therefore, the rotated figure will look as shown below.
volume of the cylinder is 1 1 3.14 8
25.12 cm3. If you overlap the two rotated figures, then the
rotated figure will look as shown below.
2 Let the length be a and the width be 3 a.

Then, when the figure is rotated as in A, the

volume of the rotated figure is (3 a) (3 a)

3.14 a 9 a a a 3.14. When the figure is

rotated as in B, the volume of the rotated figure

is a a 3.14 (3 a) 3 a a a 3.14.

9 a a a 3.14 3 3 a a a 3.14 3,
3 a a a 3.14 3 a a a 3.14

therefore the ratio of the volumes of the rotated

figures is 3 :1. 4 The surface area of the cylinder which is made by

rotating a rectangle is greater when the area of

the base gets greater and the height gets shorter.

Creative Thinking p.82~p.83 5 cm
1 cm
1 Use the cut-out section of the figure that has 1 cm

rotated around the rotation axis. 5 cm

Therefore, the greatest surface area is
(5 5 3.14) 2 (5 2 3.14 1) 188.4 cm2.

2 A ,B ,C ,D

Answer Key