Question

tyler has a box with a surface area of 62 square feet. what is the volume of the box, in cubic feet?

Explanation:

Step1: Let the width of the box be \(x\) feet.

The surface - area formula of a rectangular box \(S = 2(lw+lh + wh)\), where \(l\) is the length, \(w\) is the width, and \(h\) is the height. Given \(l = 3\) ft, \(h = 5\) ft, and \(S=62\) square feet.

$$62=2(3x + 3\times5+5x)$$

Step2: Simplify the equation.

First, divide both sides of the equation \(62 = 2(3x + 15+5x)\) by \(2\):

$$31=3x + 15+5x$$

Combine like - terms:

$$31=8x + 15$$

Subtract \(15\) from both sides:

$$8x=31 - 15$$

$$8x = 16$$

Solve for \(x\) by dividing both sides by \(8\):

$$x = 2$$

Step3: Calculate the volume.

The volume formula of a rectangular box \(V=l\times w\times h\). Substitute \(l = 3\) ft, \(w = 2\) ft, and \(h = 5\) ft into the formula:

$$V=3\times2\times5$$

$$V = 30$$

Answer:

The volume of the box is \(30\) cubic feet.