1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ganezh [65]
2 years ago
12

A regular hexagon is to be cut out of a circular sheet of metal that has a radius of 6 inches.

Mathematics
1 answer:
EleoNora [17]2 years ago
3 0

Answer:

\large \boxed{\text{D. 126.2 cm}^{2}}

Step-by-step explanation:

The area left over for scrap is the area of the circle minus the area of the hexagon.

1. Area of circle

The formula for the area of a circle is

A = πr²

A = π(6)² =  36π = 113.1 in²

2. Area of hexagon

A hexagon consists of six equilateral triangles, each of side a, and we can divide each of them into two right triangles.

So, we can calculate the area of one right triangle and multiply by 12.

The formula for the area of one triangle is

A = ½bh

(a) Height of a small triangle

Per the Pythagorean Theorem,

\begin{array}{rcr}h^{2} + 3^{2} & = & 6^{2}\\h^{2} + 9  & = & 36\\h^{2} & = & 27\\& = & 3\sqrt{3}\\\end{array}\\

(b) Area of a small triangle

A = ½ bh = ½ × 3 × 3√3 = 4.5√3 in²

(c) Area of the hexagon

The hexagon contains 12 small triangles.

A = 12 × 4.5√ 3 = 54√3 ≈ 93.53 in²

3. Area of scrap

A ≈ 113.1 in² - 93.53 in² = 19.6 in²

A = \text{19.6 in}^{2} \times \left(\dfrac{\text{2.54 cm}}{\text{1 in}}\right )^{2} = \text{126.2 cm}^{2}\\\\\text{The area of the scrap is $\large \boxed{\textbf{126.2 cm}^{\mathbf{2}}}$}

You might be interested in
Which is greater, the greatest whole number with 4 digits or the least whole number with 5 digits? Explain
mixas84 [53]
The least whole number with 5 digits is greater. The greatest number with 4 digits is 9999, and the least whole number with 5 digits is 10000. 9999 < 10000.
5 0
3 years ago
Two groups are hiking at about the same speed . Mario’s group hikes for 2.5 hours Seemas group hikes for 4.7 hours and covers 8.
amid [387]

Answer: 18.8 miles

Step-by-step explanation:

Ww are given the equation 4.7x=2.5x+8.8 to solve the question. This will be:

4.7x = 2.5x + 8.8

Collect like terms.

4.7x - 2.5x = 8.8

2.2x.= 8.8

x = 8.8/2.2

x = 4

To know how fast the kickers are going will be

4.7x = 4.7 × 4 = 18.8 miles

4 0
3 years ago
SIIOUS
I am Lyosha [343]

Answer: the distance is 8

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
What is -5(3m+4)= Please help
Naddik [55]
It would be -15m + -20
7 0
3 years ago
Read 2 more answers
Jack went to disney world and bought 4 balloons for $8.How much will 72 balloons cost?
Dennis_Churaev [7]

Answer:

144

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Other questions:
  • 1+1=?????????????????????????????????????????????????????????????? lol
    15·2 answers
  • Another geometry file upload
    15·1 answer
  • I,m trying to solve this algebra question:<br> x^+9x+20=0
    11·2 answers
  • I need help plz answer !
    11·1 answer
  • 19.83 rounded to the nearest tenth
    10·1 answer
  • Santa's workshop charges $10 to enter and $2 additional per gingerbread cookie to decorate. Choose the equation that represents
    12·2 answers
  • Sheila works with new customers or customers that want to change to a new plan. This month, she worked with 928 customers that w
    5·1 answer
  • A circle has a radius of 4ft. What is the area of the sector formed by a central angle
    10·1 answer
  • PLEASE, PLEASE HELP D:
    7·1 answer
  • A, B &amp; C form the vertices of a triangle.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!