Question
upstudy study bank question image url

Find the area of a circle if the diameter of a circle is 40 cm . (Use \( \pi \) 3.14)

Ask by Ortiz Hobbs. in the United States
Jan 29,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The area of the circle is 1256 cm².

Solution

To find the area of a circle when the diameter is given, you can use the following steps: ### Step 1: Identify the Formula The area \( A \) of a circle is given by the formula: \[ A = \pi r^2 \] where: - \( \pi \) is a constant (approximately 3.14), - \( r \) is the radius of the circle. ### Step 2: Find the Radius The radius \( r \) is half of the diameter \( d \). Given that the diameter is 40 cm: \[ r = \frac{d}{2} = \frac{40 \text{ cm}}{2} = 20 \text{ cm} \] ### Step 3: Calculate the Area Plug the radius back into the area formula: \[ A = \pi r^2 = 3.14 \times (20 \text{ cm})^2 \] \[ A = 3.14 \times 400 \text{ cm}^2 \] \[ A = 1256 \text{ cm}^2 \] ### Answer The area of the circle is **1256 cm²**.

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Beyond the Answer

To find the area of a circle, you can use the formula \( \text{Area} = \pi r^2 \). First, since the diameter is 40 cm, the radius \( r \) is half of that, which is 20 cm. Now, plug the radius into the area formula: \[ \text{Area} = 3.14 \times (20)^2 = 3.14 \times 400 = 1256 \, \text{cm}^2. \] So, the area of the circle is 1256 cm²! Understanding the area of a circle can also be fun in practical scenarios! For example, if you're designing a circular garden with a diameter of 40 cm, knowing the area lets you plan how many plants and what size flower pots to use. A common mistake when calculating the area is forgetting to halve the diameter to find the radius. Always remember to use the radius in the formula \( \text{Area} = \pi r^2 \) to avoid calculation mishaps!

Latest Geometry Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy