Question

a toy box is designed in the shape of a rectangular pyramid. the volume of the pyramid is 240 cubic centimeters, and its height from the center of the base to the apex is 12 centimeters. what is the area of the rectangular base of the pyramid? if the length of the rectangular base is 10 centimeters, what is the width of the base? use the keypad to type your answer in the box provided. the area of the rectangular base is square centimeters. the width of the base is centimeters.

Explanation:

Step1: Recall the volume formula for a rectangular pyramid

The volume formula for a rectangular pyramid is \(V=\frac{1}{3}Bh\), where \(V\) is the volume, \(B\) is the area of the base, and \(h\) is the height. We know \(V = 240\) \(cm^{3}\) and \(h=12\) \(cm\).

Step2: Solve for the area of the base \(B\)

Rearrange the formula \(V=\frac{1}{3}Bh\) to solve for \(B\). We get \(B=\frac{3V}{h}\). Substitute \(V = 240\) and \(h = 12\) into the formula: \(B=\frac{3\times240}{12}\).

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Step3: Recall the area formula for a rectangle

The area formula for a rectangle is \(B = lw\), where \(l\) is the length and \(w\) is the width. We know \(B = 60\) \(cm^{2}\) and \(l = 10\) \(cm\).

Step4: Solve for the width \(w\)

Rearrange the formula \(B=lw\) to solve for \(w\). We get \(w=\frac{B}{l}\). Substitute \(B = 60\) and \(l = 10\) into the formula: \(w=\frac{60}{10}=6\)

Answer:

The area of the rectangular base is \(60\) square centimeters.
The width of the base is \(6\) centimeters.