Problem 27 - Elementary Algebra

Question

The diameter of a circular bathroom sink is 15.75 in. Find its area. Round to the nearest tenth.

Step-by-Step Solution

Answer

The area of the sink is approximately 194.7 square inches.

Step 1: Identify the Given Information

The diameter of the circular sink is 15.75 inches.

Step 2: Find the Radius

The radius is half of the diameter. Calculate the radius using the formula: \[ r = \frac{d}{2} \] where \( d \) is the diameter. So, \[ r = \frac{15.75}{2} = 7.875 \text{ inches} \]

Step 3: Use the Area Formula

The formula for the area of a circle is: \[ A = \pi \times r^2 \] where \( r \) is the radius. Plug in the radius: \[ A = \pi \times (7.875)^2 \]

Step 4: Calculate the Area

First, square the radius: \[ (7.875)^2 = 62.015625 \] Then, multiply by \( \pi \): \[ A = \pi \times 62.015625 \] Using \( \pi \approx 3.14 \), \[ A \approx 3.14 \times 62.015625 = 194.725 \]

Step 5: Round to the Nearest Tenth

Round the calculated area to the nearest tenth: \[ A \approx 194.725 \approx 194.7 \text{ square inches} \]

Key Concepts

circle area formula

The area of a circle is a measure of the space contained within its boundary. It's important to know how to calculate this if you're dealing with circular objects like a bathroom sink. The formula to find the area of a circle is: The calculation for the area goes like this:Find the radius, square it, then multiply by pi (ewlineewlineewlineewline ewlineewlineThis gives us the formula: ewline ewlineewline ewline ewlineewline ewline ewlineA stands for area ewline ewliner stands for radius ewline ewlinePi (ewline A little tip: the symbol pi (ewline, multiply by 3.14 to solve problems quickly and easily ewline

diameter and radius relationship

Understanding the connection between the diameter and radius of a circle is crucial to minimizing errors. Here are a few keys to this concept:

The diameter is the distance from one edge of the circle to the opposite edge, passing through the center

The radius is exactly half of the diameter. It starts from the center and reaches out to the edge


If you know the diameter, you can find the radius by dividing the diameter by 2

In our example with the bathroom sink, we have a diameter of 15.75 inches
This gives us a radius of 15.75 ewline (latex– 15.75/2, which equals 7.875 inches The radius is essential because it's used in the area equation

rounding decimals

To round decimals accurately, follow these simple steps:

Identify the decimal place to which you need to round. For example, to the nearest tenth
If the digit to the immediate right of your rounding place is 5 or more, round up

If it is less than 5, round down
This process is vital to ensuring your answers are clear and concise
Applying this to our sink example: Our initial area calculation comes out as 194.725 square
Following our rounding rules, the .7 means our final answer is approximately 194.7 square inches