I need to know How do I find ab?

First photo question: Given this net of a right circular cone. Find the volume and surface area of the cone.

posledela

Problem 1

Ignore the smaller circle for now. We'll be focusing on the portion on the right.

It's a partial circle with central angle theta = 150 degrees and radius r = 24 inches. The 24 inches also happens to be the slant height of the cone when we form the 3D figure.

Let's compute the arc length based on those inputs.

L = arc length

L = (theta/360)*2*pi*r

L = (150/360)*2*pi*24

L = 20pi

This is the distance along the green curve of this portion.

Now imagine we rolled up that partial circle on the right. We'd form the curved slanted roof of the cone. The green curve wraps around to help match up with the circular base. The 20pi calculated earlier is the circumference of this circular base. Use this to find r.

C = 2pi*r

20pi = 2pi*r

r = (20pi)/(2pi)

r = 10

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So far we found that this cone has:

radius = r = 10
slant height = s = 24

Now compute the height (h) perpendicular to the base

$h^2+r^2 = s^2\\\\h = \sqrt{s^2-r^2}\\\\h = \sqrt{24^2-10^2}\\\\h = \sqrt{476}$

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We can now compute the volume

$V = (1/3)*\pi*r^2*h\\\\V = (1/3)*\pi*10^2\sqrt{476}\\\\V \approx 2284.7153\\\\$

The units of which are cubic inches.

The surface area is of this cone is:

$SA = \pi*r*s + \pi*r^2\\\\SA = \pi*10*24 + \pi*10^2\\\\SA \approx 1068.1415\\\\$

The units are in square inches.

For each case, I used the calculator's stored value of pi to get the most accuracy possible. Round the decimal values however you need to, or however your teacher instructs.

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Answers:

Volume = 2284.7153 cubic inches approximately
Surface Area = 1068.1415 square inches approximately

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Problem 2

Use the pythagorean theorem to find the slant height

$h^2+r^2 = s^2\\\\s = \sqrt{h^2+r^2}\\\\s = \sqrt{15^2+8^2}\\\\s = \sqrt{289}\\\\s = 17\\\\$

This slant height will act as the radius of the partial circle that results when forming the net of the unrolled cone.

The process used in the previous problem was to use the slant height and central angle to find the circumference of the base.

We'll follow that process in reverse to use the circumference and slant height to find the central angle.

But first, we need to find the circumference of the base.

C = 2*pi*r

C = 2*pi*8

C = 16pi

This is the arc length similar to the green arc shown in the previous problem (the figure on the right side of that diagram)

This means we'll plug in L = 16pi and r = 17 (not to be confused with the previous radius of 8 inches) to determine theta

L = (theta/360)*2*pi*r

16pi = (theta/360)*2*pi*17

16pi = theta*(34pi/360)

theta = 16pi*(360/(34pi))

theta = 169.4118 degrees approximately

This is the central angle of the unrolled net. The diagram is basically the same as the previous drawing, where we have a circle on the left to represent the base of the cone. The other portion forms the roof of the cone.

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Let's compute the volume (V) and surface area (SA)

$V = (1/3)*\pi*r^2*h\\\\V = (1/3)*\pi*8^2*15\\\\V \approx 1005.3096\\\\$

and,

$SA = \pi*r*s + \pi*r^2\\\\SA = \pi*8*17 + \pi*8^2\\\\SA \approx 628.3185$

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Answers:

Diagram: Copy the diagram shown in problem 1. However, you'll change the "24 inches" to "17 inches". Also, the central angle is roughly 169.4118 degrees.
Volume = 1005.3096 cubic inches approximately
Surface Area = 628.3185 square inches approximately

4 0

1 year ago

Is 4.05 greater than 4.2

Orlov [11]

No
4.2 is greater than 4.05
basically 4.2 is 4.20 and so 4.05 is smaller

6 0

2 years ago

Read 2 more answers

What is the distance between (8, -3) and (4, - 7) using the pathagoream theorem

Vladimir79 [104]

Answer:

Its

√

41

Step-by-step explanation: We first need to calculate the difference in x axis and in y axis:

△

x

=

8

−

4

=

4

△

y

=

7

−

2

=

5

Having this values, we now have a triangle rectangle with angles in both points. Now, just apply Pythagoras' formula:

line

2

=

△

x

2

+

△

y

2

line

2

=

4

2

+

5

2

line

=

√

41

7 0

2 years ago

Cuanto equivale una libra?

MA_775_DIABLO [31]

Huh?
Uhm I don’t understand-

4 0

2 years ago

Devin needs to fill a square pyramid that has a base of 6cm and height of 10cm,he needs to melt cubes that are 2cm by 2cm by 2cm

aleksandrvk [35]

Answer:

Three cubes

Step-by-step explanation:

Lets first write down what we know.

The dimensions of the pyramid are a base of 6cm and a height of 10cm.

The cubes are 2cm by 2cm by 2cm.

We need to find the volume of both to solve.

First, lets solve for the volume of the pyramid. The equation is Volume=base*height/3

Lets put in the values we know.

volume=6*10/3

Multiply.

volume=60/3

Divide.

volume=20cm

Now that we know the volume of the pyramid is 20cm, all we have to do is find the volume of the cubes, and then divide 20cm by their volume.

To find the volume of the cubes, we just need to multiply length, width, and height together.

2cm*2cm*2cm=8cm

Now divide 20cm by 8cm.

20/8=2.5 rounding up to 3.

Devin will need to melt 3 cubes to fill the square pyramid.

Hope this helps!

3 0

2 years ago