Question

example 3 find the area of a rectangular solid (prism) with length of 3 2/7 in, width of 6 in, and height of 11 in.

volume = length x width x height
= 3 2/3 in. x 6 in. x 11 in.
= 11/3 · 6/1 · 11/1
11 · 2 · 11 = 22 · 11
= 242 cu.in.

exercises: find the volume of each figure below. unless you use a calculator, show your work.

1.)

volume = area of base x height
= length x width x height
v = _ x _ x ___
= ___ cubic in.

2.)

show your work.
volume =

find the volume of each figure described in the table below.

show work below, especially on problems 4 and 6 which involve fractions. if you use a scientific calculator, you do not have to show the work.

Explanation:

Step1: Calculate the volume of the first rectangular prism (Problem 1)

The formula for the volume of a rectangular prism is \(V = l\times w\times h\). Here, \(l = 8\) in, \(w=6\) in, \(h = 3\) in.
\(V=8\times6\times3\)
\(V = 144\) cubic in.

Step2: Calculate the volume of the second rectangular prism (Problem 2)

Using the formula \(V=l\times w\times h\), with \(l = 3\) yd, \(w = 2\) yd, \(h=6.5\) yd.
\(V=3\times2\times6.5\)
\(V=39\) cubic yd.

Step3: Calculate the volume for Problem 3

Using \(V=l\times w\times h\), \(l = 8\) in, \(w = 6\) in, \(h=3\) in.
\(V=8\times6\times3=144\) \(in^{3}\)

Step4: Calculate the volume for Problem 4

First, convert \(7\frac{1}{2}=\frac{7\times2 + 1}{2}=\frac{15}{2}\) ft.
Using \(V=l\times w\times h\), \(l=\frac{15}{2}\) ft, \(w = 4\) ft, \(h = 6\) ft.
\(V=\frac{15}{2}\times4\times6\)
\(V=15\times2\times6\)
\(V = 180\) \(ft^{3}\)

Step5: Calculate the volume for Problem 5

Using \(V=l\times w\times h\), \(l = 3.2\) cm, \(w=3.2\) cm, \(h = 4\) cm.
\(V=3.2\times3.2\times4\)
\(V = 40.96\) \(cm^{3}\)

Step6: Calculate the volume for Problem 6

Convert \(3\frac{1}{2}=\frac{3\times2+1}{2}=\frac{7}{2}\) ft and \(2\frac{1}{2}=\frac{2\times2 + 1}{2}=\frac{5}{2}\) ft.
Using \(V=l\times w\times h\), \(l=\frac{7}{2}\) ft, \(w=\frac{5}{2}\) ft, \(h = 1\) ft.
\(V=\frac{7}{2}\times\frac{5}{2}\times1=\frac{35}{4}=8.75\) \(ft^{3}\)

Answer:

1. \(144\) cubic in.
2. \(39\) cubic yd.
3. \(144\) \(in^{3}\)
4. \(180\) \(ft^{3}\)
5. \(40.96\) \(cm^{3}\)
6. \(8.75\) \(ft^{3}\)