Advanced Placement (AP) College

Answer the questions below to find the total surface area of the can. A can with radius 2.5 inches and height 5 inches. 2 circles with radius 2.5 inches on opposite sides of a rectangle with width 5 inches. Find the area of the circles at the top and bottom of the can. The area of each circle is exactly π square inches. There are identical circles in the cylinder. So the total area of all the circles is π square inches. Find the area of the rectangular label. One side of the rectangle is π in. The other side of the rectangle is inches. The area of the rectangle is exactly π square inches. Find the total surface area of the tomato ketchup can. The total surface area is exactly π square inches.

Answers

Answer 1

The total surface area of the tomato ketchup can is determined as 37.5 π in².

Total surface area of the can

The can be modeled as a cylinder and the total surface area is calculated as follows;

T.S.A = 2(area of circles) + 2(Curved surface area) or area of rectangle

T.S.A = 2πr² + 2πrh

Area of each circle in π square inches

A = πr²

A = (2.5)²π

A = 6.25π in²

Total area of the circles

A = 2(6.25π in²) = 12.5 π in²

Area of the rectangle

A = 2πrh

A = 2(2.5)(5)π

A = 25 π in²

Total surface area of the can

A = 12.5 π in² + 25 π in²

A = 37.5 π in²

Thus, the total surface area of the tomato ketchup can is determined as 37.5 π in².

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