Answer:42 square meters.
Step-by-step explanation:
To calculate the surface area of a right circular cylinder, you need to find the areas of its two circular bases and the lateral surface area (the rectangle that wraps around the cylinder).
Given that the net of the right circular cylinder is 4 m, 8 m, 4 m, we can deduce that the 8 m dimension represents the circumference of the circular base since it's the only dimension that could be circular. The height of the cylinder would be the remaining dimension, which is 4 m.
Let's calculate:
The radius (r) of the circular base can be found by dividing the circumference by
2
�
2π:
2
�
�
=
8
2πr=8
�
=
8
2
�
≈
8
6.28
≈
1.27
m
r=
2π
8
≈
6.28
8
≈1.27 m
The area of each circular base is
�
�
2
πr
2
:
�
base
=
�
(
1.27
)
2
≈
5.07
m
2
A
base
=π(1.27)
2
≈5.07 m
2
The lateral surface area of the cylinder is the circumference of the circular base times the height:
�
lateral
=
2
�
�
×
ℎ
A
lateral
=2πr×h
�
lateral
=
2
�
×
1.27
×
4
≈
31.81
m
2
A
lateral
=2π×1.27×4≈31.81 m
2
Now, add the areas of the two circular bases and the lateral surface area to find the total surface area:
�
total
=
2
×
�
base
+
�
lateral
A
total
=2×A
base
+A
lateral
�
total
=
2
×
5.07
+
31.81
≈
41.95
m
2
A
total
=2×5.07+31.81≈41.95 m
2
Rounded to the nearest whole number, the surface area is approximately 42 square meters.
