The 4th time of me posting this question

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

Alexxx [7]

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 $37\frac{1}{2} \cdot \pi$ 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;

$r = \dfrac{C}{2 \cdot \pi}$

Which gives;

$r = \dfrac{5 \cdot \pi}{2 \cdot \pi} = \dfrac{5}{2} = 2.5$

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.

$Volume \ of \ a \ cone = \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h$

Therefore;

$V = \dfrac{1}{3} \times \pi \times 2.5^2 \times 18 = 37\frac{1}{2} \cdot \pi$

The volume of the cone, V = $37\frac{1}{2}$ ·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:

brainly.com/question/17023854

4 0

3 years ago

A halogen-lighting manufacturer packs 64 halogen lamps ink a cube-shaped container. the manufacturer has been asked by his distr

pishuonlain [190]

64 divided by 8 = 8

So you're answer would be 8

4 0

3 years ago

Move point b some more as you move point b the angle formed between ab and cd varies if you want to make an perpendicular to cd

dybincka [34]

Answer:

Following are the response to the given question:

Step-by-step explanation:

Move b a bit further if the angle between cd and ab changes when you move b if you want to make a perpendicular point to cd The angle BEC is 90 ° for making the AB line perpendicular to the line CD to transfer point B to the angle between the two lines.

8 0

3 years ago

The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed

OlgaM077 [116]

Answer:

Test is Left tailed test

Parameter tested is standard deviation

Step-by-step explanation:

We are given the hypothesis as;

Null hypothesis; H0: σ = 8.6

Alternative hypothesis; H1: σ < 8.6

Where;σ is a constant generally known in statistics as the standard deviation.

Now, it's the alternative hypothesis that will let us know whether this is left tailed, right tailed or two tailed.

Alternative hypothesis says σ < 8.6.

This means that the values of σ that satisfy this hypothesis are less than 8.6 and thus are on the left hand side of 8.6 on a number line. Thus, the shaded region in a normal distribution curve will be on the left.

Thus, it's a left tailed test

3 0

3 years ago

What is the equation of the line in slope-intercept form? y=_x+_

tangare [24]

Answer:

$y=\frac{4}{3}x+4$

Step-by-step explanation:

4 0

3 years ago