Question

5. If the tree's circumference is 141.3ft, what is its diameter?

Answer 1

Answer:

d ≈ 45 ft

General Formulas and Concepts:

Symbols

• π (pi) ≈ 3.14

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right  

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Geometry

• Circumference of a Circle Formula: C = πd

Step-by-step explanation:

Step 1: Define

Circumference C = 141.3 ft

Step 2: Solve for d

1. Substitute in C [Circumference Formula]:                                                       141.3 ft = πd
2. Substitute in π (approximation):                                                                      141.3 ft ≈ 3.14d
3. [Division Property of Equality] Divide both sides by 3.14:                              45 ft ≈ d
4. Rewrite:                                                                                                             d ≈ 45 ft

Answer 2

Diagram:

$\setlength{\unitlength}{1mm}\begin{picture}(50,55)\linethickness{0.4mm}\qbezier(45,30)(45,30)(5,30)\qbezier(25.000,10.000)(33.284,10.000)(39.142,15.858)\qbezier(39.142,15.858)(45.000,21.716)(45.000,30.000)\qbezier(45.000,30.000)(45.000,38.284)(39.142,44.142)\qbezier(39.142,44.142)(33.284,50.000)(25.000,50.000)\qbezier(25.000,50.000)(16.716,50.000)(10.858,44.142)\qbezier(10.858,44.142)( 5.000,38.284)( 5.000,30.000)\qbezier( 5.000,30.000)( 5.000,21.716)(10.858,15.858)\qbezier(10.858,15.858)(16.716,10.000)(25.000,10.000)\multiput(5,30)(20,0){3}{\circle*{1}}\end{picture}$

Given:

↬ Circumference of circle = 141.4 ft

To find:

↬ diameter of circle

Solution:

To find diameter first we should know value of radius.

As:-

$\boxed{\boxed{ \sf{}Radius = \frac{diameter}{2}}}$

So first let's find value of radius.

we know:-

$\bigstar \boxed{ \sf{Circumstances =2\pi r}}$

By using this formula we can find value of radius.

$\dashrightarrow\sf{Circumstances =2\pi r}$

$\dashrightarrow\sf{141.3 =2 \times \dfrac{22}{7} \times r}$

$\dashrightarrow\sf{ \dfrac{1413}{10} =2 \times \dfrac{22}{7} \times r}$

$\dashrightarrow\sf{ \dfrac{1413}{10} \times \dfrac{7}{22} \times \dfrac{1}{2} =r}$

$\dashrightarrow\sf{ \dfrac{1413 \times 7}{10 \times 22 \times 2}=r}$

$\dashrightarrow\sf{ \dfrac{9891}{10 \times 22 \times 2}=r}$

$\dashrightarrow\sf{ \dfrac{9891}{440}=r}$

$\dashrightarrow\sf{ r = \dfrac{9891}{440}}$

$\dashrightarrow\sf{ r =22.48~inches} \textsf{ \textbf{(approx)}}$

Now let find diameter:

As we know:

$\boxed{\boxed{ \sf{}Radius = \frac{diameter}{2}}}$

Therefore:

$: \implies{}\sf{}Radius = \dfrac{diameter}{2}$

$: \implies{}\sf{}22.48 = \dfrac{diameter}{2}$

$: \implies{}\sf{} \dfrac{diameter}{2} = 22.48$

$: \implies{}\sf{} diamete r= 22.48 \times 2$

$: \implies{}\sf{} diamete r= 44.96 ~inches$

$\therefore\underline\textsf{diameter of tree is \textbf{45 inches (approx)}}$