The roof of a tower in a castle is shaped like a cone. The height of the roof is 30 ft, and the radius of the base is 15 ft. What is the area of the roof? What is the lateral area of the roof?

Answers

Answer 1

Answer:

The area of the roof: ≈2287.44 ft^2, the lateral area of the roof:≈1580.58 ft^2

Step-by-step explanation:

The area of the roof is computed by the equation of the area of a cone:
A = πr(r + [tex]\sqrt{h^{2}+r^(2) }[/tex])
(r: radius, h: height, πr^2 is the area of the base of the cone, πr[tex]\sqrt{h^{2}+r^(2) }[/tex] is the lateral area of the cone). So:

A = [tex]15\pi (15 + \sqrt{30^{2} +15^{2} } )[/tex] ≈ 2287.44 ft^2.

As I stated earlier, the lateral area of the roof can be computed:

A[tex]L[/tex]=[tex]15\pi \sqrt{30^{2} +15^{2} }[/tex] ≈ 1580.58 ft^2.


Related Questions

CAN SOMEBODY HELP ME PLEASE

Answers

Answer:

(A) P(t) = 220t - 435 390

(B) predicted moose population = 6370

Step-by-step explanation:

the longer working shows the explanation and working for part A while the shorter working is for part B

hi i need help thank u so much

WORTH 5o points

Answers

Answer:

it will be 8 answer letter A

Answer:

A. 8

Step-by-step explanation:

From pythagoras theorem

10^2=6^2+x^2

100-36=x^2

sqrt 64=x

x=8

how many part time and full time employees does the company have?

Answers

Answer:

there are 36 part time employees and there are 144 full time employees

Step-by-step explanation: multiply 45 by 4

then multiply 180 by 0.2 to get 36 and 180 by 0.8 and get 144

If line segment AB is 400​%, what is the length of a line segment that is ​100%?

Answers

the length of the line would be 1 inch

Can Someone Assist Me Please? It would be much appreciated​

Answers

Ya sure.... What's your doubt?

b^2 – 4ac if a = 2, b = 9, and c = 4

Answers

Answer:

49

Step-by-step explanation:

[tex](b)^{2} - 4(a)(c) \\(9)^{2} - 4(2)(4) \\81 - 4(2)(4) \\81 - 32 \\49[/tex]

Find the equation of the line that goes to the point (8,-8) that is perpendicular to the line with the equation of y=2/7 x - 26 ​

Answers

Step-by-step explanation:

line equation

y = ax + b

a is the slope, b is the y-intercept.

a slope perpendicular to another slope flips x and y upside down and flips the sign.

so, the slope perpendicular to 2/7 is -7/2.

so, our desires line function looks like

y = -7/2 × x + b

to get b we use the given point (and it's x and y coordinates = values).

-8 = -7/2 × 8 + b = -7×4 + b = -28 + b

b = 20

so, the full line equation is

y = -7/2 × x + 20

Let y=6 and z=2. Translate “z less than y” into an algebraic expression and solve it

Answers

Answer:

y - z; 6 - 2; 4

Step-by-step explanation:

z less than y means subtract z from y

y - z

Substitute the given values.

6 - 2

4

Triangle ABC is isoceles and has a perimeter of 20cm.Sides AB and AC are each twice as long as BC. Calculate the length of the side BC

Answers

Answer:

length of the side BC=4

Step-by-step explanation:

length of the side BC = x

length of the side AB = 2x

length of the side AC = 2x

x + 2x + 2x = 20

5x=20

x=4

      BC = 4

AB=8

AC=8

  8+8+4=20

Solve For X.

6x + 9 - 4x = -3

Answers

Answer:

x = -6

Step-by-step explanation:

6x + 9 - 4x = -3

2x +9 = -3

2x = -12

x = -6

Plsss help mee I’m not sure what the answer is

Answers

So r = 5
Base area = pi * r ^ 2 = pi * 5 ^2 = 25 pi
Volume = base area * height = 25 pi * 20 = 500 pi
D

Answer:

D. would be the correct answer

The points plotted below are on the graph of a polynomial. In what range of x- a values must the polynomial have a root? Check all that apply. A. -2 to -1 B. -1 to 0 C. -3 to-2 D. 1 to 2 E. -4 to -3 F. O to 1​

Answers

a b f e are the answer because you multiply then divide

Hey ! Can anyone help me solve these problems please. Thank you !

Answers

[tex] \qquad\begin{gathered} \begin{array}{ ||c|| c} \hline \\ \textsf { \huge{ \underline{lets\: \: solve}}} \\ \\ \: \: \sf6. \: \underline{ find \: measure \: of \: angle \: TSR}\: \: \\ \\ \textsf {As we know, diameter subtends 90° } \\ \textsf{ at an arc of same circle.} \\ \textsf{ hence we can conclude that :} \\ \\ \rm{ \therefore\angle \:TSR = 90 \degree } \\ \\ \\ \sf7. \: \underline{ find \: measure \: of \: angle \: subtended }\\ \: \underline{ \sf by \: arc \: ST \: at \: the \: centre \: of \: circle}\: \\ \\ \\ \textsf{Angle subtended by an arc at centre} \\ \textsf{ of the circle is double the angle} \\ \textsf{ subtended by the same arc on other } \\ \textsf{ part of circle, hence we can} \\ \textsf{conclude that :} \\ \\ \sf\angle SOT =2 \angle SRT \\ \\ \angle \sf SOT =2 \times 41\degree \\ \\ \sf \therefore\angle SOT = 82 \degree \\ \\ \\ \\ \hline \end{array} \end{gathered}[/tex]

which functions graph is the widest parabola A. y=1/8x^ B.y=3x^ C. y=1/3x^ D. y=8x^

Answers

We look for the one with the least coefficient of x²:

[tex] \frac{1}{8} = 0.125[/tex]

[tex]3 = 3[/tex]

[tex] \frac{1}{3} = 0.333[/tex]

[tex]8 = 8[/tex]

Answer:y=1/8 x²

Answer:

A. y=1/8x^

Step-by-step explanation:

on
Find the distance between -1/2 and 1 2/3
on
a number line.

units

Answers

Answer:

Step-by-step explanation:

1 2/3 -(-1/2)

=5/3+1/2

[tex]=\frac{10+1}{6} \\=\frac{11}{6} \\=1\frac{5}{6}[/tex]

This recipe makes 4 pancakes.
Sanjay follows the recipe but wants to make 12 pancakes.
How much of each ingredient does he need?

Recipe: Makes 4
135 g flour
1 teaspoon (tsp) baking powder
2 tablespoons (tbsps) sugar
130 ml milk
1 egg
2 tablespoons (tbsps) oil

Answers

Answer:

405g of flour, 3 teaspoons baking powder, 6 tablespoons sugar, 390ml of milk and 3 eggs and 6 tablespoons of oil

Step-by-step explanation:

She wants to triple the recipe, so she must multiply each amount of each ingredient by three:

135 × 3 = 405

1 × 3 = 3

2 × 3 = 6

130 × 3 = 390

1 × 3 = 3

2 × 3 = 6

What is the mean (average) of
a, a, b, b, b,c

Answers

Answer:

Ans might be a+b+c

Step-by-step explanation:

Hope the picture will help

if f(-3)=14 what would be the equation for f(x)

Answers

Answer:

Step-by-step explanation:

if quadratic

(-3)²+5=9+5=14

so f(x)=x²+5

or

if linear

(-3)+17=14

f(x)=x+17

if  cubic

(-3)³-2(-3)²-3(-3)+14=14

f(x)=x³-2x²-3x+14

so on.


A Goodyear Blimp is positioned at a height of 1,500 feet over the M&T
Bank Stadium to broadcast the Baltimore Ravens game. The blimp is
observed by a car of fans as they look upward at an angle of 22º.
Another car closer to the stadium can see the blimp if they look
upward at an angle of 65º.
DEOOV
כשע
Figure not
drawn to scale
1500 ft
65
22
x ft.
Determine x, the distance between the two cars.

Answers

The distance between two cars comes to be 4412.06 feet.

Find the attached diagram to visualize it better.

From the attached diagram

The Distance between two cars is x+y

The angle of elevation for the first car = 22 degrees

The angle of elevation for the second car = 65 degrees.

Height of the Goodyear blimp = 1500 feet

What is the tangent of an angle?

The tangent of an angle is the ratio of the opposite side to the adjacent side of that angle.

So, tan 22° = 1500/x

So, x= 1500/tan 22°

x = 3712.63 feet

tan 65° = 1500/y

So, y = 1500/tan 65°

y = 699.46 feet

x+y = 4412.06 feet

So, the distance between two cars =  4412.06 feet

Therefore, the distance between two cars comes to be 4412.06 feet.

To get more about the angle of elevation visit:

https://brainly.com/question/10217662

The proof that ΔEFG ≅ ΔJHG is shown.

Given: G is the midpoint of HF, EF ∥ HJ, and EF ≅ HJ.

Prove: ΔEFG ≅ ΔJHG

Triangles E F G and J H G share common point G.


Statement

Reason
1. G is the midpoint of HF 1. given
2. FG ≅ HG 2. def. of midpoint
3. EF ∥ HJ 3. given
4. ? 4. alt. int. angles are congruent
5. EF ≅ HJ 5. given
6. ΔEFG ≅ ΔJHG 6. SAS What is the missing statement in the proof?

∠FEG ≅ ∠HJG
∠GFE ≅ ∠GHJ
∠EGF ≅ ∠JGH
∠GEF ≅ ∠JHG

Answers

Answer: ∠GFE ≅ ∠GHJ

Step-by-step explanation:

In triangle EFG, we have side FG (which is opposite angle E) and EF (the side opposite angle G).

For SAS, we need the angle in between these sides, which would be angle F.

Answer:

B.∠GFE ≅ ∠GHJ

Step-by-step explanation:

got it correct on my quiz

Roberto's science grade is calculated using a weighted average. Quizzes are worth 25%, homework is worth 10%, unit tests are worth 30%, and labs are worth 35%.

Roberto earned an average of 94% on his quizzes, 99% on his homework, 92% on his unit tests, and 94% on his labs.


What is Roberto's final science grade?


93.3%

93.9%

94.8%

95.3%

Answers

Answer: the answer is 93.9

I hope this helps

Step-by-step explanation:

i know it its on k12

Answer:

93.9

Step-by-step explanation: I took the k12 test

simplify the following 42÷7+14-4×5​

Answers

Answer:

1

Step-by-step explanation:

42/7 + 14 - 4 × 5

7 + 14 - 4 × 5

7 +14 - 20

20 - 20

0

Answer:0

because 42 divided by 7 is 6 and 6 + 14 is 20 and 4 times 5 is 20 som then 20 -20 = 0

Drew and Beau each brought cylindrical water bottle to football practice. Drew's water bottle has a diameter of 3 inches and a height
of 7 inches. Beau's water bottle has a radius of 2 inches and a height of 9 inches. Whose water bottle holds more water and how much more does it hold? Round to the nearest hundredth.

Answers

The bottle that holds more water has the larger volume

Beau's water bottle holds more water

How to determine the bottle with more water?

The given parameters are:

Drew

Diameter = 3 inchesHeight = 7 inches

Beau

Radius = 2 inchesHeight = 9 inches

The volumes of their bottles is calculated using:

V = πr^2h

So, we have:

Drew = 3.14 * (3/2)^2 * 7

Drew = 49.46

Beau = 3.14 * (2)^2 * 9

Beau = 113.04

By comparison, 113.04 is greater than 49.46

Hence, Beau's water bottle holds more water

Read more about volumes at:

brainly.com/question/1972490

Write the value of (2 +√ 2) (2 -√3)

Answers

[tex]\left(2 + \sqrt 2 \right)\left(2-\sqrt 3 \right)\\\\=4- 2\sqrt 3 + 2 \sqrt 2 - \sqrt 6\\\\=0.91484.....[/tex]

Find all the factors of 12.
A) 2, 3, 4, 6
B) 2, 3, 4, 6, 12
C) 1, 2, 3, 4, 6, 12

Answers

the answer is B cause it’s b

Answer:

1, 2, 3, 4, 6, and 12, because each of those divides 12 without leaving a remainder (or each of those is a counting number that can be multiplied by another counting number to make 12).

Step-by-step explanation:

hope this helps.

the ratio of the corresponding edge lengths of two similar solids is 4;9 what is the ratio of their volume ?

Answers

Answer:

Do the math

Step-by-step explanation:

If you do the math you get answer

Diego is flying from Philadelphia to Barcelona. On the trip to Barcelona, the plane flies at a constant cruising
speed of 550 mph.
reaches its cruising speed, which is
On the trip home, Diego makes a chart of the plane's progress once
constant
Which is faster the cruising speed on the flight from Philadelphia to Barcelona, or the cruising speed on the flight home?
Hour
1
2
3
A
Miles
530
1060
1590
US
Choose 1 answer:
Со
The cruising speed on the flight from Philadelphia to Barcelona
The cruising speed on the flight home
Pro
Pro
© The two cruising speeds are the same.

Answers

The faster speed is the cruising speed on the flight from Philadelphia to Barcelona.

Which speed is faster?

Average speed is the total distance travelled per time. It is used to determine how fast an object is moving with respect to time.

Average speed = total distance / total time

Average speed on the flight back home = 530 / 1 = 530 mph

To learn more about average speed, please check: https://brainly.com/question/21734785

Felix is dividing 322 by 12. He says the answer is going to be smaller than 322.
Do you agree with him and why?

Answers

Answer:  Because dividing means to split into smaller groups

Two of the interior angles of a triangle are 84.0° and 30.0. Find the measure of the
third interior angle in degrees to one decimal place.

Answers

Answer:

66.0°

Step-by-step explanation:

The sum of the measures of the interior angles in a triangle is 180°.

Let "x" represent the measure of the third interior angle. We can use this to set up an equation:

84.0° + 30.0° + x = 180°

Add like terms:

114.0° + x = 180°

Subtract 114.0° from both sides:

x = 66°

The question asks for the answer to be in degrees to one decimal place, therefore:

x=66.0°

Becket needs to solve the system of equations using elimination.
-2x+4y=-2
(6x-y=28)
Which correctly describes the first step Becket should take?
A. Multiply each term in the 1st equation by -3
B. Multiply each term int he 1st equation by 3
C. Multiply each term in the 2nd equation by -4
D. Both B and C would work

Answers

Answer:

B. Multiply each term in the 1st equation by 3

Step-by-step explanation:

A is incorrect because multiplying the entire 1st equation by -3 will give you 6x - 12y = 6. This does not cancel with either x or y term in the second equation.B is correct because by multiplying the entire 1st equation by 3 will give you -6x + 12y = -6. The -6x term will cancel (or eliminate) the 6x term in the second equation.C is incorrect because multiplying the entire 2nd equation by -4 will give you -24x + 4y = -112. This does not cancel with either x or y term in the 1st equation.D is incorrect because C was proven to be incorrect.

Step-by-step explanation:

step 1

Multiply each term in the second equation with 4

step 2

Add equation 1 to equation 2

step 3

make x subject of formula and obtain value of X

step 4

substitute value of X in equation 1 and find Y

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