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Chapter 1: Problem 29

A stick of butter at \(35^{\circ} \mathrm{F}\) measures 1.25 in. \(\times 1.25\) in. \(x\) 4.65 in. and weighs 4 ounces. Find its specific weight.

Short Answer

Expert verified
To calculate the specific weight of the butter, first convert all measurements to compatible units: inches to feet and ounces to pounds. Then calculate the volume of the butter using the product of its given dimensions, and subsequently calculate the specific weight by dividing the weight by the volume.

Step by step solution

01

Convert the Dimensions to Comparable Units

First, let's convert the dimensions of the butter, given in inches, to feet. We'll use the conversion: 1 inch = 0.08333 feet. So, the dimensions in feet are: \(1.25 in. \times 0.08333 = 0.10416 ft\), \(1.25 in. \times 0.08333 = 0.10416 ft\), \(4.65 in. \times 0.08333 = 0.38737 ft\).
02

Calculate the Volume

Next, calculate the volume of the butter using the formula for the volume of a rectangular box V = lwh, where l = length, w = width, h = height. Here, the volume will be \(V = 0.10416 ft \times 0.10416 ft \times 0.38737 ft\). Calculate the value to get the volume of the butter.
03

Convert Weight into Compatible Unit

Now, convert the weight of butter given in ounces to pounds, because that's the usual unit in which specific weight is expressed. To do this, use the conversion: 1 ounce = 0.0625 pounds. Therefore, the weight in pounds is \(4 oz \times 0.0625 = 0.25 lb\).
04

Calculating Specific Weight

Now that we have both the volume and the weight in compatible units we can calculate the specific weight. The specific weight, represented by the symbol γ, is calculated by dividing weight by volume. So in this case, \(\gamma = W/V\). Use the values calculated in steps 2 and 3 to finish the calculation.

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