Question

volume = length x width x height
2.
volume = 90 in³
x=
3.
volume=
=
4.
volume = 98 cm³
y=
5.
volume = 60 ft³
z=
6.
volume=
=

Explanation:

Step1: Calculate the volume of the first rectangular prism

Use the formula \(V = l\times w\times h\). Here \(l = 4\) in, \(w = 4\) in, \(h=6\) in.
\(V=4\times4\times6\)
\(V = 16\times6=96\) in³

Step2: Find the height \(x\) of the second rectangular prism

Given \(V = 90\) in³, \(l = 6\) in, \(w = 3\) in. Use the formula \(V=l\times w\times h\), so \(h=\frac{V}{l\times w}\)
\(x=\frac{90}{6\times3}=\frac{90}{18} = 5\) in

Step3: Calculate the volume of the third rectangular prism

Given \(l = 8\) m, \(w = 3\) m, \(h = 7\) m. Use \(V=l\times w\times h\)
\(V=8\times3\times7=24\times7 = 168\) m³

Step4: Find the width \(y\) of the fourth rectangular prism

Given \(V = 98\) cm³, \(l = 7\) cm, \(h = 2\) cm. Use \(h=\frac{V}{l\times w}\), so \(y=\frac{98}{7\times2}=\frac{98}{14}=7\) cm

Step5: Find the length \(z\) of the fifth rectangular prism

Given \(V = 60\) ft³, \(w = 4\) ft, \(h = 7.5\) ft. Use \(l=\frac{V}{w\times h}\)
\(z=\frac{60}{4\times7.5}=\frac{60}{30}=2\) ft

Step6: Calculate the volume of the sixth cube

Given \(l = w=h = 9\) in. Use \(V=l\times w\times h\)
\(V=9\times9\times9=81\times9 = 729\) in³

Answer:

1. \(96\) in³
2. \(x = 5\) in
3. \(168\) m³
4. \(y = 7\) cm
5. \(z = 2\) ft
6. \(729\) in³