Question

to the nearest cubic inch, what is the volume of the small milk carton shown? 65 in³ 88 in³ 63 in³ 44 in³

Explanation:

Step1: Calculate the volume of the rectangular prism

The formula for the volume of a rectangular prism is \(V = l\times w\times h\). Here, \(l = 3\) in, \(w = 3\) in, \(h = 6.5\) in. So, \(V_{prism}=3\times3\times6.5 = 58.5\) \(in^{3}\).

Step2: Calculate the volume of the triangular prism

The formula for the volume of a triangular prism is \(V=\frac{1}{2}\times b\times h\times l\). Here, \(b = 3\) in, \(h = 1.5\) in, \(l = 3\) in. So, \(V_{triangular}= \frac{1}{2}\times3\times1.5\times3=\frac{1}{2}\times13.5 = 6.75\) \(in^{3}\).

Step3: Calculate the total volume

Add the volumes of the two prisms: \(V_{total}=V_{prism}+V_{triangular}=58.5 + 6.75=65.25\approx65\) \(in^{3}\).

Answer:

\(65\ in^{3}\)