Login
Premium
Home Question Bank Math Geometry
Question
upstudy study bank question image url

The diameter of a circle is 6 cm . Find its area to the nearest tenth

Ask by Dawson Osborne. in the United States
Mar 14,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The area of the circle is approximately 28.3 cm².

Solution

1. The diameter of the circle is \(6\) cm, so the radius \(r\) is half of the diameter: \[ r = \frac{6}{2} = 3 \text{ cm} \] 2. The area \(A\) of a circle is given by the formula: \[ A = \pi r^2 \] 3. Substitute the radius into the formula: \[ A = \pi (3)^2 = 9\pi \] 4. Using the approximation \(\pi \approx 3.1416\), calculate the area: \[ A \approx 9 \times 3.1416 = 28.2744 \text{ cm}^2 \] 5. Rounding to the nearest tenth: \[ A \approx 28.3 \text{ cm}^2 \]

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Extra Insights

To find the area of a circle, you can use the formula A = πr², where r is the radius. Since the diameter is 6 cm, the radius (r) is half of that, which is 3 cm. Now, plugging in the values, the area (A) would be A = π(3 cm)² = 9π cm². Approximating π as 3.14, the area is about 28.3 cm² when rounded to the nearest tenth. Fun fact: The first known calculation of the area of a circle dates back to ancient Egypt, around 1650 BC, where they used a formula that approximated the value of π. Isn't it fascinating how this simple geometric shape has sparked mathematical curiosity for centuries? In real-world applications, understanding the area of a circle can be quite valuable! For instance, if you’re tiling a circular fountain, knowing the precise area helps you calculate how many tiles you’ll need. Or, if you’re planting a round flower bed, it ensures your plants have enough space to thrive!

Related Questions

Question What is the image point of \( (2,-4) \) after the transformation \( r_{y=x} \circ T_{0,0} \) ?
Geometry United States Mar 15, 2025
A) triangle has these properties: - three sides of different lengths - two angles that are less than \( 90^{\circ} \) and one angle that is greater than \( 90^{\circ} \) Which words describe the triangle? 4)) isosceles, acute scalene, obtuse (d)) scalene, acute isosceles, obtuse
Geometry United States Mar 15, 2025
(1)) Which sentence is true? A)) All rhombuses have 2 pairs of parallel sides. A)) All rhombuses have 4 right angles. A)) All parallelograms have 4 right angles. All parallelograms have 4 equal sides.
Geometry United States Mar 15, 2025
Vectors Exercise 5.4 1. Let \( \mathbf{u}=(11,16) \) and \( \mathrm{v}=(-8,12) \). Find \( \begin{array}{llll}\begin{array}{ll}\text { a. } \mathbf{5 u} & \text { b. } \mathbf{3}(4 \mathbf{u})\end{array} \quad \text { c. }(5+\mathbf{3}) \mathbf{u} & \text { d. } \mathbf{4}(\mathbf{u}+\mathrm{v}) & \text { e. } 1 \cdot v \quad \mathrm{f} .0 \cdot \mathrm{v}\end{array} \) 2. In the triangle \( \mathrm{ABC}, \overrightarrow{A B} \) represents \( \mathbf{u} \) and \( \overrightarrow{B C} \) represents v . If D is the midpoint of AB , then express \( \overrightarrow{A C}, \overrightarrow{C A} \) and \( \overrightarrow{\mathrm{DC}} \) in terms of \( \mathbf{u} \) and v .
Geometry Ethiopia Mar 16, 2025
A geometric problem applicable to primary school children is one that can be a. represented, analyzed, and possibly solved, using the methods of mathematics. b. represented and analyzed using the methods of mathematics. c. analyzed and solved using the methods of mathematics d. solved using the methods of mathematics
Geometry Guyana Mar 16, 2025

Latest Geometry Questions

Exercise \( 5 \cdot 3 \) \( \begin{array}{l}\text { 1. Find } \quad \text { a. } u+v \\ \text { ifu }=(3,4), \quad \mathbf{v}=(5,-1) \\ \text { ( andw }=(2,-5) . \\ \text { 2. Write any point } A, B, C \text { and } F \text { in your notebook and draw diagrams to illustrate } \\ \text { the following vector equations: } \\ \begin{array}{lll}\text { a. } \overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{BC}}=\overrightarrow{\mathrm{AC}} & \text { b. } \overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{BC}}+\overrightarrow{\mathrm{CF}}=\overrightarrow{\mathrm{AF}} & \text { c. } \overrightarrow{\mathrm{AB}}-\overrightarrow{\mathrm{BC}}=\overrightarrow{\mathrm{AC}}\end{array} \\ \text { 3. Graphically add the given vectors } \mathbf{u} \text { and } \mathbf{v} \text { shown in Figure } 5.14 \text { by using head to }\end{array} \)
Geometry Ethiopia Mar 16, 2025
Vectors Exercise 5.4 1. Let \( \mathbf{u}=(11,16) \) and \( \mathrm{v}=(-8,12) \). Find \( \begin{array}{llll}\begin{array}{ll}\text { a. } \mathbf{5 u} & \text { b. } \mathbf{3}(4 \mathbf{u})\end{array} \quad \text { c. }(5+\mathbf{3}) \mathbf{u} & \text { d. } \mathbf{4}(\mathbf{u}+\mathrm{v}) & \text { e. } 1 \cdot v \quad \mathrm{f} .0 \cdot \mathrm{v}\end{array} \) 2. In the triangle \( \mathrm{ABC}, \overrightarrow{A B} \) represents \( \mathbf{u} \) and \( \overrightarrow{B C} \) represents v . If D is the midpoint of AB , then express \( \overrightarrow{A C}, \overrightarrow{C A} \) and \( \overrightarrow{\mathrm{DC}} \) in terms of \( \mathbf{u} \) and v .
Geometry Ethiopia Mar 16, 2025
\( 3.14 \cdot ( 40 cm ) ^ { 2 } \)
Geometry United States Mar 16, 2025
A geometric problem applicable to primary school children is one that can be a. represented, analyzed, and possibly solved, using the methods of mathematics. b. represented and analyzed using the methods of mathematics. c. analyzed and solved using the methods of mathematics d. solved using the methods of mathematics
Geometry Guyana Mar 16, 2025
28 How many diagonals are there in a 12-sided convex polygon?
Geometry Guyana Mar 16, 2025
Prev Next
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