Question

muriel jenkens
to whom it may concern,
i would like to purchase several planter boxes, all with a height of 5 inches. can you make one that holds 100 cubic inches of dirt? please contact me at your earliest convenience.
thank you,
muriel jenkens
reply forward
6 write a response to this customer, showing all calculations.

Explanation:

Step1: Recall the volume formula

The volume \(V\) of a rectangular prism (planter box) is \(V = l\times w\times h\), where \(l\) is length, \(w\) is width, and \(h\) is height. Given \(h = 5\) inches and \(V=100\) cubic inches.

Step2: Solve for the base area

We can rewrite the formula as \(V=A\times h\) (where \(A = l\times w\) is the base area). Then \(A=\frac{V}{h}\). Substitute \(V = 100\) and \(h = 5\): \(A=\frac{100}{5}=20\) square inches.

Step3: Provide examples of length and width

Since \(A=l\times w = 20\), possible pairs \((l,w)\) are \((1,20)\), \((2,10)\), \((4,5)\) (in inches).

Answer:

Dear Muriel Jenkens,

We can make a planter box that holds 100 cubic inches of dirt. The volume formula for a rectangular - shaped planter box is \(V=l\times w\times h\). Given \(h = 5\) inches and \(V = 100\) cubic inches.

First, we find the base area \(A\) (where \(A=l\times w\)). Using \(V = A\times h\), we substitute \(V = 100\) and \(h = 5\): \(A=\frac{V}{h}=\frac{100}{5}=20\) square inches.

Some possible dimensions (length \(l\) and width \(w\)) for the base (since \(l\times w=20\)) are:

• \(l = 1\) inch and \(w = 20\) inches
• \(l = 2\) inches and \(w = 10\) inches
• \(l = 4\) inches and \(w = 5\) inches

Thank you for your inquiry.

Best regards,
[Your Name]