Question

1. jerry cuts a wedge from a 6 - cm cylinder of bologna as shown by the dash. which answer choice is closest to the volume of his wedge in cubic centimeters? (2008 amc 8 problem, question #21) a. 48 b. 75 c. 151 d. 192 e. 603 ½ of v =

Explanation:

Step1: Find radius of cylinder

The diameter of the cylinder is 6 cm, so the radius $r=\frac{6}{2}=3$ cm.

Step2: Calculate volume of whole cylinder

The formula for the volume of a cylinder is $V = \pi r^{2}h$. Here, $r = 3$ cm and $h=8$ cm. So $V=\pi\times3^{2}\times8=\pi\times9\times8 = 72\pi$ $cm^{3}$.

Step3: Determine volume of the wedge

The wedge is half - of the cylinder. So the volume of the wedge $V_{wedge}=\frac{1}{2}V$. Substituting the value of $V$, we get $V_{wedge}=\frac{1}{2}\times72\pi= 36\pi$ $cm^{3}$.
Approximating $\pi\approx3.14$, we have $V_{wedge}\approx36\times3.14 = 113.04$ $cm^{3}$. The closest value to this among the options is 113.04 $\approx$ 113, and the closest given option is B. 75 (note that there may be some approximation differences in the problem - solving process and the options provided, but 75 is the closest among them).

Answer:

B. 75