Video: Calculating the Specific Gravity of a Cube of Zinc of Given Its Width and Mass and the Density of Water

A solid cube of zinc with the width of 6.0 inches has a mass of 56 lbs. What is the specific gravity of this sample of zinc? Water weighs 62 pounds per cubic foot. [A] 0.0042 [B] 0.14 [C] 0.24 [D] 1.5 [E] 7.2

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Video Transcript

A solid cube of zinc with the width of 6.0 inches has a mass of 56 pounds. What is the specific gravity of this sample of zinc? Water weighs 62 pounds per cubic foot. A) 0.0042, B) 0.14, C) 0.24, D) 1.5, or E) 7.2.

The specific gravity is a ratio between the density of your sample and the density of a reference material. In this case, the reference material is water. If the specific gravity is less than one, the substance will float on the reference material. And if the specific gravity is greater than one, the substance will sink in the reference material. So, to find the specific gravity and solve this problem, we need to first find both the density of zinc and the density of water.

Remember that density is equal to the mass of an object divided by its volume. Luckily for us, the density of water was given in this problem. It’s 62 pounds per cubic foot. So, all we have to do before we can find the specific gravity is find the density of zinc. The mass of zinc is given in the problem as 56 pounds. Now, we need to calculate the volume of the zinc.

We’re told that our zinc sample is a solid cube with a width of six inches. So, we can find the volume of our cube by cubing the width. But the density of water is given in units of pounds per cubic foot. And we’re going to need the density of zinc and the density of water to cancel. So, before we find the volume of our zinc cube, let’s first convert the width of the cube from inches into feet.

We can do this by dividing the width of our cube by 12 inches because there’s 12 inches in one foot. Six divided by 12 is one-half. So, the width of our cube is half a foot. Now, we can find the volume of our cube by cubing the width. This gives us one-eighth of a cubic foot. Now, we can put this in to find the density of zinc.

We can either divide 56 by one-eighth or we can flip the fraction on the bottom so we can multiply 56 by eight. No matter which way you do it, you’ll find that the density of zinc is 448 pounds per cubic foot. Now, we have everything we need to find the specific gravity of the sample of zinc.

Dividing 62 into 448 is quite hard to do in our head. But if we look through the answer choices, they’re pretty spaced out, so we can round these two numbers to make the math easier. So, let’s round the numerator to 450 and the denominator to 60, which we can simplify to 45 over six. There are two numbers around 45 that are divisible by six. Six can go into 48 eight times. And six can go into 42 seven times. This means that the specific gravity for our sample of zinc should be between seven and eight.

Since the specific gravity of our zinc cube is greater than one, we know that zinc will sink and not float in water. If we look through our answer choices, the only one that’s between seven and eight is answer choice E, which is 7.2. So, the specific gravity of our zinc cube is 7.2.

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