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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

The shape of a solid wire can be approximated by a cylinder, where the circular cross section of the wire represents the base of the cylinder and the length of the wire represents the height of the cylinder. If a wire has a circular base with a diameter of 0.01 meters and a length of 31.42 meters, what is the total volume of the wire, to the hearest hundredth of a cubic centimeter?

A. 0.01
B. 785.5
C. 2468
D. 9871

答案和解析

答案：C

解析：

Choice C is correct. The equation for the volume of a cylinder is V= πr^2h, where V is the volume, r is the base radius, and h is the height. In this problem, the height is the length of the wire.

The radius of the wire is half the diameter, so r=0.01/2=0.005 meters. This must be converted to centimeters, by mulyiplying 0.005 by 100 to get 0.5 centimeters. The length of the wire, h, is 31.42 meters. This must be converted to centimeters by multiplying 31.42 by 100 to get 3142 centimeters. To find the volume, substitute these values in and simplify V= π(0.25)(3142)=2468. The correct answer is 2468 cubic centimeters.