Question

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