The correct answer is 94.4πsquare inches
To calculate the total surface area of the labeled soup can, you need to consider the areas of the two circular bases and the rectangular label.
Area of the circular bases:
The formula for the area of a circle is
A=πr^2 ,
where
r is the radius.
The area of one circular base is
π×(4^2 )=16π square inches.
Since there are two circular bases, the total area of both bases is
2×16π=32π square inches.
Area of the rectangular label:
The area of a rectangle is
A=length×width.
The length of the rectangle is the same as the circumference of one of the circular bases (since the label wraps around the can), and the width is the height of the rectangle.
The circumference of a circle is C=2πr, so the length of the rectangle is 2π×4=8π inches.
The height of the rectangle is given as 7.8 inches.
The area of the rectangular label is 8π×7.8=62.4π square inches.
Total surface area:
Add the areas of the circular bases and the rectangular label to find the total surface area.
32π+62.4π=94.4π square inches.
Therefore, the correct answer is 94.4πsquare inches
Question
A label is placed around a soup can during manufacturing. If the label is represented by the rectangle in the figure, how many square inches is the label? Answer in terms of π.
image of a net drawing of a cylinder is shown as two circles each with a radius labeled 4 inches and a rectangle with a height labeled 7.8 inches
94.4π square inches
32π square inches
30.1π square inches
62.4π square inches