Solve the systems of equations:
1 answer:
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Answer:
or 12.57
Step-by-step explanation:
or 12.57
The Halloween conical hat, with given height, circular base and brim
extension has the following calculated parameters;
Part a. The slant height is <u>18.2 inches</u>
Part b. The volume of the cone is in.³
Part c. The area of the brim, <em>A</em> = <u>36·π in.²</u>
Part d. The area of the brim is found by <u>subtracting the area of the base of the cone from the area covered by the perimeter of the brim</u>
Reasons:
Known parameters;
Height of the conical portion, h = 18 inches
Base circumference, C = 5·π inches
Part a. Slant height of the conical portion; Required
Solution:
The circumference of a circle, C = 2·π·r
Therefore;
Which gives;
Radius, r = 2.5 inches
According to Pythagoras's theorem, we have; s² = r² + h²
Where;
s = The slant height of the cone
s² = 2.5² + 18² = 330.25
s = √(330.25) ≈ 18.2
- The slant height, <em>s</em> ≈ <u>18.2 inches</u>
Part b. The measure in cubic inches of candy that exactly fills the conical portion of the hat is the volume of the cone.
Therefore;
- The volume of the cone, V =
·π in.³
Part c. The extension of the brim from the base of the cone = 4 inches
The radius of the brim, R = Radius of the base of the cone + 4 inches
∴ <em>R</em> = 2.5 inches + 4 inches = 6.5 inches
Area of the brim, <em>A</em> = Area of the 6.5 inch circle - Area of the circular base of the cone
∴ A = π × 6.5² - π × 2.5² = 36·π
- The area of the brim, <em>A</em> = <u>36·π in.²</u>
Part d. The procedure for solving the question in part c, is described as follows;
- The area of the brim can be found by finding the entire area of the circle formed by the perimeter of the brim, then subtracting the area of the base of the cone from that area.
Learn more here:
Answer: 2
Step-by-step explanation: To find the greatest common factor or GCF of 8 and 18, we begin by finding all of the factors of each number.
To find the factors of 8, we know that 8 ÷ 1 is 8 so 1 and 8 are factors.
8 ÷ 2 is 4 so 2 and 4 are factors.
However, if we continue to divide 8 by 3, 4, 5, and so on, we won't find any new factors. So the factors of 8 are 1, 2, 4, and 8.
Now let's find the factors of 18.
18 ÷ 1 is 18 so 1 and 18 are factors.
18 ÷ 2 is 9 so 2 and 9 are factors.
18 ÷ 3 is 6 so 3 and 6 are factors.
However, if we continue to divide by 4, 5, 6, and so on, we won't find any new factors. So the factors of 18 are 1, 2, 3, 6, 9, and 18.
Now that we have our list of factors, to find the greatest common factor, we simply find the largest number that is shared by the two lists.
Notice that our lists share a 1 but the largest number they share is a <em>2</em><em>.</em>
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So the greatest common factor or <em>gcf</em> of 8 and 18 is 2.
I have also shown my work on the whiteboard.
