what is the volume of the part shown? 2.69 in.³ 2.80 in.³ 2.89 in.³ 3.00 in.³

Explanation:

Step1: Calculate volume of large - block

The large - block can be considered as a combination of two rectangular prisms. One has dimensions (1\times1\times0.5) and the other has dimensions (2\times0.5\times0.5). The total volume of the large - block without holes (V_{total - block}= (1\times1\times0.5)+(2\times0.5\times0.5)=0.5 + 0.5=1) (in the first part) and (V_{total - block}=1+(1\times1\times0.5)=1.5) (in the second part), and the overall volume of the large - block (V_{total - block}=2\times1\times1 = 2) in³.

Step2: Calculate volume of first hole

The first hole has a diameter (d_1 = 0.38) in, so the radius (r_1=\frac{0.38}{2}=0.19) in and length (l_1 = 1) in. The volume of a cylinder (V_{cylinder}=\pi r^{2}l). So the volume of the first hole (V_1=\pi\times(0.19)^{2}\times1\approx3.14\times0.0361\times1 = 0.1134) in³.

Step3: Calculate volume of second hole

The second hole has a diameter (d_2 = 0.5) in, so the radius (r_2=\frac{0.5}{2}=0.25) in and length (l_2 = 1) in. The volume of the second hole (V_2=\pi\times(0.25)^{2}\times1=3.14\times0.0625\times1 = 0.1963) in³.

Step4: Calculate net volume

The net volume of the part (V = V_{total - block}-V_1 - V_2=2-(0.1134 + 0.1963)=2 - 0.3097=2.6903\approx2.69) in³

Answer:

A. (2.69) in.³