Question

a microwave oven has a capacity of 1.59ft³. the interior of the microwave of the is 14 in wide and 14 in deep. what is the height of the interior of the microwave, to the nearest tenth of a foot​

Answer 1

Step-by-step explanation:

The easiest way to do this is to imagine the microwave as a box. Ignore the turntables, whether or not something will spin if it touches an edge, and anything else that would make the fact that we're talking about a microwave confusing. This is a box now. :)

The capacity of our box is 1.59 ft^3, which means it can hold that much of "things" inside it. Instead of a capacity, we'll think of it as the box's total area. A tricky thing to note, is the area is given in ft, where the interior values are given as inches. So we'll need to turn the inches into feet.

To get the area of a box, we do length x width x height.

We're already given the length, 14 (inches), and the width, 14 (inches), so all we need to find now is the height (feet). To turn the lengths into feet, we'll divide them by 12, because there are 12 inches in 1 foot, or Feet = Inches / 12.

To finally turn it into math:

Area (A) = length (L) * width (W) * height (H)

$A = L * W * H$

Insert known values.

$1.59 = \frac{14}{12} * \frac{14}{12} * H$

Multiply.

$1.59 = \frac{196H}{144}$

Simplify.

$1.59 = \frac{49H}{36}$

Multiply both sides by 36.

$1.59*36 = \frac{49H}{36}*36$

Simplify.

$57.24 = 49H$

Divide both sides by 49.

$\frac{57.24}{49} = \frac{49H}{49}$

Simplify.

$1.16816326... = H$

To turn make this the nearest Tenth, we round up to the first decimal place.

Answer:

H = 1.2 ft