Use 3.14 for π. Round each value to the nearest whole unit....

Use 3.14 for $\pi .$ Round each value to the nearest whole unit. Sam bought an aboveground circular swimming pool with diameter 27 ft and height 54 in. a. Approximate the volume of the pool in cubic feet using 3.14 for $\pi .$ b. How many gallons of water will it take to fill the pool? (Hint: 1 gal $\approx 0.1337 \mathrm{ft}^{3}$ )

Use 3.14 for $\pi .$ Round each value to the nearest whole unit.
Sam bought an aboveground circular swimming pool with diameter 27 ft and height
54 in.
a. Approximate the volume of the pool in cubic feet using 3.14 for $\pi .$
b. How many gallons of water will it take to fill the pool? (Hint: 1 gal $\approx 0.1337 \mathrm{ft}^{3}$ )

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Key Concepts

Volume Conversion Factor

A volume conversion factor allows for the translation of volume measurements from one unit to another, such as converting cubic feet to gallons. This step is crucial for contextualizing results in units that are practically relevant, such as water storage or usage.

Rounding

Rounding is the process of simplifying a number to a specified degree of precision, such as to the nearest whole unit. This is important in practical applications where overly precise numbers are unnecessary and could complicate interpretation.

Unit Conversion

Unit conversion involves standardizing measurements so that all dimensions are in the same units. This is critical when a problem includes mixed units, such as inches and feet, to ensure that calculations are accurate and coherent.

Cylinder Volume Formula

The cylinder volume formula, V = ?r²h, is essential for calculating the volume of any cylindrical shape. It combines the area of the circular base (?r²) with the height of the cylinder, giving a clear method for determining the space inside the cylinder.

Transcript

00:01 All right, so i've got an above ground pool.

00:06 Pretend that looks like a circle.

00:08 So that's going to give us a cylinder.

00:11 And we know that this diameter all the way across is 27.

00:26 And this height is 54 inches.

00:32 So the first thing that we have to do is decide which units to get these in.

00:37 Do we want it in inches or feet? and since they're telling us they want us to find the volume in cubic feet, the first thing i want to do is take that 54 inches and convert it to feet.

00:48 So if you haven't done dimensional analysis in a while, that's usually the easiest way to remember what you're going to do.

00:56 So i know that there are 12 inches, and the reason i put the inches in here in the bottom is because i want this to cancel, because i want to be left with those feet.

01:10 And so there's 12 inches in one foot.

01:20 So that gives me 4 .5 feet tall for this.

01:24 Pool.

01:31 So now i want to fill it up with water.

01:34 I want to find out how much volume that is in cubic feet.

01:39 So the volume of my pool is pi r squared h.

01:50 So substituting in, we're going to use 3 .14 for pi.

02:01 But they give me diameter, not radius...