The base area of a right circular cone is 1/4 of its total surface area. What is the ratio of the radius
to the slant height?

Answers

Answer 1

Given:

The base area of a right circular cone is [tex]\dfrac{1}{4}[/tex] of its total surface area.

To find:

The ratio of the radius  to the slant height.

Solution:

We know that,

Area of base of a right circular cone = [tex]\pi r^2[/tex]

Total surface area of a right circular cone = [tex]\pi rl+\pi r^2[/tex]

where, r is radius and l is slant height.

According to the question,

[tex]\pi r^2=\dfrac{1}{4}(\pi rl+\pi r^2)[/tex]

Multiply both sides by.

[tex]4\pi r^2=\pi rl+\pi r^2[/tex]

[tex]4\pi r^2-\pi r^2=\pi rl[/tex]

[tex]3\pi r^2=\pi rl[/tex]

Cancel out the common factors from both sides.

[tex]3r=l[/tex]

Now, ratio of the radius  to the slant height is

[tex]\dfrac{r}{l}=\dfrac{r}{3r}[/tex]

[tex]\dfrac{r}{l}=\dfrac{1}{3}[/tex]

Therefore, the ratio of the radius  to the slant height is 1:3.


Related Questions

Help please for brainliest

Answers

48 I just took the test :) you’re welcome

please help me solve this equation i need step by step explaining 3x + 2= x+4(x+2)

Answers

The answer is x= -3
Remove the ()
Collect terms
Move variable to the left hand side and change its sign
Move variable to the right hand side and change its sign.
Collect like terms
Subtract the numbers
Divide both sides of the equation by -2
And your solution should be x= -3

Anyone help? Please I’ve tried -35 but the graph is just to ten

Answers

Answer:

f(x) is always 5.

Step-by-step explanation:

The formula has a fixed value. Y is the f(x) in the function, and since there is no X, then Y is as said: 5. For example, when X is -7, the f(x), or Y, is still 5, and so on.

3. Determine if the graph below is a function.
Explain your reasoning.

Answers

Answer:

A function defines one variable in terms of another. The statement "y is a function of x" (denoted y = y(x)) means that y varies according to whatever value x takes on. A causal relationship is often implied (i.e. "x causes y"), but does not *necessarily* exist.

Step-by-step explanation:

Factor tree for 14 i reeaallyy

Answers

Answer:

I need points lol well I kinda have no idea what ur taking abt

Answer:

the calculator i used was called calculator soup this is a website all u gotta do is search up factor calculator and it will pop up this website always helps if u want u can search up what u calculator u want at the top where it says search

How do I write Domain and Range in inequality notation?

Answers

Answer:

Step-by-step explanation:To combine two intervals using inequality notation or set-builder notation, we use the word “or.” As we saw in earlier examples, we use the union symbol, \displaystyle \cup∪, to combine two unconnected intervals. For example, the union of the sets \displaystyle \left\{2,3,5\right\}{2,3,5} and \displaystyle \left\{4,6\right\}{4,6} is the set \displaystyle \left\{2,3,4,5,6\right\}{2,3,4,5,6}. It is the set of all elements that belong to one or the other (or both) of the original two sets. For sets with a finite number of elements like these, the elements do not have to be listed in ascending order of numerical value. If the original two sets have some elements in common, those elements should be listed only once in the union set. For sets of real numbers on intervals, another example of a union is

Please help me out! Help me please! This is so important!

The ratio of girls to boys in a primary school is 4:5. If there are 24 girls, how many boys are there? Help!

Answers

Answer:

there are 30 boys

Step-by-step explanation:

If there is 24 girls you divide that by 4 and you get six so that means you multiply with six and you get 30.

A ratio of 4:5 means that for every 4 girls, there are 5 boys.

24 girls / 4 girls = 6

5 * 6 = 30 boys

There are 30 boys if there are 24 girls

Write the equation of the line that passes through the points (-9, -3) and (-7, 7). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line. क Answer: Submit Answer attempt out of 2 Type here to search O in G​

Answers

Answer:

5x-y +42=0

Step-by-step explanation:

Using m=Y2- Y1

X2- X1

the slope of the line is found .

Put your answer in Y - Y1 = m( X - X1)

to get the equation

Naomi bought a dress on sale for $24. Naomi bought the dress for 60% of the original price. Which equation shows how to find the original cost of the dress?

A.
0.60x = 24


B.
0.40x = 24


C.
24x = 60


D.
60 – 24 = x

Answers

Answer:

A

Step-by-step explanation:

what is 35% as a fraction

Answers

Answer:

7/20

Step-by-step explanation:

Question 8
A log with diameter 60 cm is 3 m in length its hollow centre is 20 cm in diameter.

Find the surface area of the log in cm', including the ends and the inside, correct to one decimal place.

Answers

Answer:

The surface area of the log including the ends and the inside is 80424.8 cm²

Step-by-step explanation:

To determine the surface area of the log with hollow center including the ends and the inside, we will find the surface area of the outer part of the log, surface area of the inner part of the log and the surface area of the two ends; and then sum everything up.

From the question,

Diameter of log = 60 cm

Length of log = 3 m = 300 cm

Diameter of hollow center = 20 cm

For the surface area of the outer part,

Area of the outer part = Circumference of the outer part × length

Circumference = 2πr = πd

∴ Area of the outer part = πd × l

(NOTE: d here is the diameter of the log)

d = 60 cm and l = 300 cm

Area of the outer part = 60π × 300 = 18000π cm²

For the surface area of the inner part,

Area of the inner part = Circumference of the inner part × length = πd × l

(NOTE: d here is the diameter of the hollow center)

d = 20 cm and l = 300 cm

Area of the inner part = 20π × 300 = 6000π cm²

For the surface area of one end

This is the difference between the area of the outer end and the area of the inner end

Here, we can determine the area by using

Area = πr², where r is the radius

Radius = Diameter / 2

Radius of outer end (R) = Diameter of log / 2 = 60cm / 2 = 30cm

Radius of inner end (r) = Diameter of hollow center / 2 = 20cm / 2 = 10 cm

∴ Surface area of one end = πR² - πr² = π(R²-r²)

= π (30²-10²)

= π (900 - 100)

= 800π cm²

This is the area of one end

For the two ends,

Area of the two ends = 2 × 800π cm² = 1600π cm²

Hence, the surface area of the log is 18000π cm² + 6000π cm² + 1600π cm²

Surface area of the log = 25600π cm²

Putting the value of π (π = 3.141592654)

Surface area of the log = 25600 × 3.141592654 cm²

Surface area of the log = 80424.77193 cm²

Surface area of the log = 80424.8 cm²

Hence, the surface area of the log including the ends and the inside is 80424.8 cm² (to one decimal place)

6. Doug has been evicted from his home. He sits on the street corner with a homemade
sign asking people to give him food. Doug is wearing only shorts and a t-shirt in the
snowy afternoon. Doug plays his harmonica in hopes of attracting some donors. One
kind soul brings him a cup of hot chocolate. A passerby yells at Doug to "Get a job!"
upsetting Doug so much that he spills the steaming hot chocolate on his leg.

Answers

What do u mean by this question?

SOMEONE PLEASE HELP QUICK

Answers

X can be any number in the graph as long as it is on the x-axis therefore you can put x as -1,0 and 1. Then you would need to replace the ‘x’ in the equation so it would look like y=-2*1+3. You replace ‘x’ with every number you put in the x boxes. Then just solve the equations

y=-2*1+3
Y=-2*0+3
Y=-2*-1+3
They would give you the y axis coordinates so then you just put them together for the middle column.

Answer

y=-2*1+3=1
Y=-2*0+3=3
Y=-2*-1+3=5

Coordinates are (1,3) (0,3) (-1,5)

A car wash detailed 132 cars in 4 hours. How many cars did they detail per hour?

Answers

Answer:

33 Cars

Step-by-step explanation:

132 / 4 = 33

Therefore,

The answer is,

33 Cars

2. Solve in two ways
1/2 +1/4

Answers

Answer:

Step-by-step explanation: the first time you get 0.75 and the second time you get 0.125 hope this helped

Which of the following is equal to the opposite of −45?

−|45|
−|−45|
−(−45)
−45








Which of the following statements does not represent the same value as the others?

the absolute value of 9
the absolute value of negative 9
the opposite of 9
the distance between 0 and −9











All of the following are true statements except _____.

|−93| = −93
|−93| = 93
−|93| = −93
|93| = 93













If you move from zero to 15 on the number line, you are representing all of the following except _____.

the absolute value of 15
the distance between zero and 15
the opposite of −15
the opposite of 15














All of the following expressions are equal to N except _____.

−(− N )
− N
| N |
|− N |

Answers

Answer:

The first one

Step-by-step explanation:

1. -(-45)
2. “The opposite of 9”
3. -93
4. “ the opposite of 15”
5. -N

What is the answer for number 7

Answers

Answer: (C) Non-linear; not a function Explanation:

Martin charges $15 for every 5 bags of leaves he rakes last weekend he raked 20 bags of leaves how much money did he earn

Answers

Answer:

60 hope this helps

Step-by-step explanation:

15 divided by 5 =3

20 multiplied by 3 =60

Convert 2 days into months. Round your answer to the nearest hundredth.

Answers

Answer:

0.0657534

Step-by-step explanation:

divide 2 by 30.417

RS¯¯¯¯¯¯ bisects ∠QRT. If m∠QRT = 116°, what is m∠QRS?

A. 26°
B. 232°
C. 64°
D. 58°

Answers

Answer:

D. 58

Step-by-step explanation:

pretty easy clap

bisecting is midpoint which makes the two angles congruent

Use the limit definition to find an equation of a tangent line of f(x)= 1/(x-1) at the given point (2,1)

Answers

By "limit definition", I assume you mean the derivative. We have

[tex]f'(c) = \displaystyle\lim_{x\to c}\frac{f(x)-f(c)}{x-c}[/tex]

For [tex]f(x)=\frac1{x-1}[/tex] and c = 2, we have

[tex]f'(2)=\displaystyle\lim_{x\to2}\frac{\frac1{x-1}-1}{x-2}[/tex]

[tex]f'(2)=\displaystyle\lim_{x\to2}\frac{\frac{1-(x-1)}{x-1}}{x-2}[/tex]

[tex]f'(2)=\displaystyle\lim_{x\to2}\frac{2-x}{(x-1)(x-2)}[/tex]

[tex]f'(2)=\displaystyle\lim_{x\to2}\frac1{1-x}=-1[/tex]

The tangent line to (2, 1) has slope -1. Using the point-slope formula, it has equation

y - 1 = - (x - 2)

y = - x + 3

a pizzeria had 4 cans of tomato sauce how many pizzas could they make with the cans if each pizza took one fourth of a can​

Answers

Answer:

16 pizzas.

Step-by-step explanation:

That is 4 divided by 1/4

= 4 * 4/1

= 16.

Answer:

16

Step-by-step explanation:

There are 4 pizzas per can and you have 4 cans.

4 x 4 = 16

If a polygon is a pentagon, then it has 5 sides hypothesis conclusion

Answers

Answer:

Hypothesis

 

Step-by-step explanation:

 a polygon has five sides Conclusion: it is a pentagon If a polygon has five sides, then it is a pentagon.

hope this helps

A math class consists of 26 students, 14 women, 10 men, and 2 non-binary. Two students are selected at random to participate in a probability experiment. Compute the probability that:

Answers

Answer:

there's a higher probability for females

Round 24.9652 to
1 decimal Place​

Answers

Answer:

2.5 one decimal rounding off means to make it to one decimal place.the no is 24.9652 if you want to round of then you have to put decimal after 2 only then it will be one decimal place .this is because when we see a number after the point greater than 5 then we add 1 to the right side .now if we add 1 to the right side of 24.9652 by rounding off and making it to one decimal place then it will be 2.5.

Find the value of x.

(A) 16 (B) 41 (C) 5 (D) 25 (E) 66

Answers

Answer:

D. 25

Step-by-step explanation:

D. 25 is the correct answer....Hopes it helps you....Hopes to get BRAINLIEST.. .

Thank you ☺️☺️☺️

In my opinion answer is 25 or D

7) Order the numbers from least to greatest.
A. 6.66
B. 6.07
C. 7
D. 6.32

Answers

the Answear is B,D,A,C

Use inductive reasoning to predict the next three numbers in the pattern.

Home

3, 5, 8, 13, 21, 34, ...

nents

Predict the next three numbers in the pattern.

3, 5, 8, 13, 21, 34,

Answers

Answer:

The next three terms are 55,89 and 144

Step-by-step explanation:

We want to predict the next three numbers in the pattern

3, 5, 8 , 13 , 21 , 34

The difference between two successive terms is written between them.

Thus, we have

3 2 5 3 8 5 13 8 21 13 34

So the rule here is to add the next term to the previous so as to get the next coming term

Thus, we have;

34 + 21 = 55

55 + 34 = 89

89 + 55 = 144

Which coordinate pair is a solution of the linear
equation below?
-X + 3y = 21
Click on the correct answer.
(3,-8)
(-3,8)
(3,8)

Answers

Answer:

slope is 4/3 and y intercept is -7

Step-by-step explanation:

3y+21=4x.........now subtract 21 from each side

3y=4x-21......now divide all terms by 3

y=%284%2F3%29x-7......there ya go ...slope is 4/3 and y intercept is -7

Answer:

B (-3,8)

Step-by-step explanation:

awnser A is incorrect because if you switch out the x for 3 and the y for -8. The equation would look like -3+3×(-8)=21. and after multiplying 3×-8 which equals -24. The equation turns into -3+(-24)=21 . And after adding -3 and -24 you get -27=21

awnser B is correct because if you switch out the x for -3 and the y for 8. The equation would look like -3+3×8=21. After multiplying 3×8 which equals 24. The equation turns into -3+24=21. And after adding -3and 24 which is pretty much subtracting you get 21=21.

Best apologies if incorrect

point Q was rotated about the origin (0,0) by 180

Answers

Answer:B

Step-by-step explanation:

The coordinates of the image of the rotation of the point Q is:

Q' = (4, 2)

What is the image of the rotation?

We can see that the original coordinates of point Q are (-4, 0).

If we apply a rotation of 180° about the point (0, 0), it is equivalent to a reflection around the y-axis.

It only changes the sign of the x-component.

Then the image of the rotation is:

Q' = (4, 0)

If you want to learn more about rotations:

https://brainly.com/question/4289712

#SPJ2

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