AMC 8 Daily Practice Round 7

Complete problem set with solutions and individual problem pages

Problem 19 Easy

There is a cylindrical part with a height of 10 centimeters and a base diameter of 6 centimeters. One end of the part has a straight cylindrical hole, as shown in the figure: the diameter of the circular hole is 4 centimeters, and the depth of the hole is 5 centimeters. If the parts of this component that are exposed to air are to be painted with anti-rust paint, what is the total area to be painted in square centimeters?(For convenience, use \pi = 3.14.)

  • A.

    282.6

  • B.

    292.02

  • C.

    307.72

  • D.

    326.56

  • E.

    320.28

Answer:C

The total area to be painted includes the outer surface area of the cylinder, the inner surface area of the hole, and the area of the two circular bases (adjusted for the hole).

The calculation is as follows: 3.14 \times \left(\frac{6}{2}\right)^2 \times 2 + 3.14 \times 6 \times 10 + 3.14 \times 4 \times 5 = 307.72

The total area to be painted is 307.72 square centimeters.

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