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If you can solve all parts I will give brainliest (also give strategy)

part a. Gretchen is going to make a witch’s hat for Halloween. Her pattern consists of a right circular cone without a base attached to a circle with a hole cut out of the middle, as shown in attached pic. The hole is congruent to the base of the cone.



Gretchen plans to make the conical portion of her hat 18 inches tall with a base circumference of 5pi inches. What is the slant height of the conical portion of the witch hat if made according to Gretchen’s plan? Express your answer as a decimal to the nearest tenth.



part b. Gretchen’s completed hat looks great. Unfortunately, when she tries to put her hat on, she realizes it is too small! When she double checks the dimensions, she finds that they are exactly as she had planned so she must have measured incorrectly in the beginning. Not wanting to waste the great looking hat, she decides to use it to put candy in. How many cubic inches of candy will exactly fill the conical portion of the hat? Express your answer as a common fraction in terms of pi.



part c. If the brim of Gretchen’s hat is a ring that extends 4 inches out from the base of the conical portion, what is the area of the brim in square inches? Express your answer in terms of pi.



part d. Pick one question above and describe your strategy for solving.

If you can solve all parts I will give brainliest also give strategy part a Gretchen is going to make a witchs hat for Halloween Her pattern consists of a right class=

Respuesta :

The Halloween conical hat, with given height, circular base and brim

extension has the following calculated parameters;

Part a. The slant height is 18.2 inches

Part b. The volume of the cone is [tex]37\frac{1}{2} \cdot \pi[/tex] in.³

Part c. The area of the brim, A = 36·π in.²

Part d. The area of the brim is found by subtracting the area of the base of the cone from the area covered by the perimeter of the brim

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;

[tex]r = \dfrac{C}{2 \cdot \pi}[/tex]

Which gives;

[tex]r = \dfrac{5 \cdot \pi}{2 \cdot \pi} = \dfrac{5}{2} = 2.5[/tex]

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, s ≈ 18.2 inches

Part b. The measure in cubic inches of candy that exactly fills the conical portion of the hat is the volume of the cone.

[tex]Volume \ of \ a \ cone = \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h[/tex]

Therefore;

[tex]V = \dfrac{1}{3} \times \pi \times 2.5^2 \times 18 = 37\frac{1}{2} \cdot \pi[/tex]

  • The volume of the cone, V = [tex]37\frac{1}{2}[/tex]·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

∴ R = 2.5 inches + 4 inches = 6.5 inches

Area of the brim, A = 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, A = 36·π in.²

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:

https://brainly.com/question/17023854

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