The volume of a rectangular prism with a cone shaped hole in it is approximately 163.22cm³ (as shown below).
✏️ What is the height of the cone?

The Volume Of A Rectangular Prism With A Cone Shaped Hole In It Is Approximately 163.22cm (as Shown Below).

Answers

Answer 1

Answer:

Height of the cone = 5 cm

Step-by-step explanation:

Volume of the rectangular prism with a cone shaped hole = Volume of the rectangular prism - Volume of the cone

Volume of the rectangular prism = Length × Width × Height

                                                       = 5 × 5 × 7

                                                       = 175 cm³

Volume of the cone = [tex]\frac{1}{3}\pi r^{2}h[/tex]

Here, r = Radius of the cone

h = Height of the cone

Volume of the cone = [tex]\frac{1}{3}\pi (\frac{3}{2})^{2}(h)[/tex]

                                 = 0.75πh cm³

Volume of the rectangular prism with a hole = 163.22 cm³

175 - 0.75πh = 163.22

0.75πh = 175 - 163.22

0.75πh = 11.78

h = 5 cm


Related Questions

8 to the 9th power over 8 to the 7th power simplified?

Answers

Answer:

64

Step-by-step explanation:

8^9/8^7

Subtract the 9 and 7 which equals 2

Which is 8^2

8^2 is 64

Thus the answer is 64

Hope this helps!

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Answers

Answer:

A

Step-by-step explanation:

-|x+3| has a x-intercept of -3. A is the only option with -3 as an x-intercept.

-hope it helps

Answer:

answer be A

Step-by-step explanation:

Evaluate the expression when b=5 and y=-2. b-8y ​

Answers

Substitute the numbers in place of the variables. (5)-8(-2)—> 5+16–>21. Answer is 21. Can I get brainliest?
ubstitute the variables with the numbers. 5+16->21 = (5)-8(-2). The correct answer is 21.

Which system of equations has no soulutions

Answers

A because it is touching the origin

Help. I can’t seem to figure out what to do

Answers

Answer: Both of the Givens go in the left top boxes, and then in the right top boxes you would put B is the midpoint of AD and CE and then AC is equal to DE. In the third and fourth boxes on the left, you would put CB = EB and then AB is equal to DB. In the third and fourth boxes on the right you put both of the Def. of Midpoints. Then, in the last box to the left, you would put triangle ABC = DBE. In the final box to the right you would put Side-Side-Side Congruency.

Step-by-step explanation:

1) ac≅de, given

2) b is the midpoint, given

3) ab≅db, defn midpoint

4) cb≅eb, defn midpoint

5) abc≅dbe, side side side

Eric leaves his house on his bike. He rides at a constant speed until he reaches a lemonade stand, where he parks his bike and takes a rest. Then he turns around and bikes home as fast as he can.

Answers

Answer: What's even the question? It's not asking anything to solve

Step-by-step explanation:

The cafe sells Beetle Juice and Potion Punch. A cup of Beetle Juice costs $2.50 and a cup of Potion Punch costs $3. Owen ordered 5 drinks for his group and spent $14. Write a system of equations to find the number of cups of beetle juice, j, and potion punch, p, that Owen purchased.

Answers

Answer:

2  Beetle juices and 3 Potion Punch

Step-by-step explanation:

j = Beetle Juice       cost $2.50

p = Potion Punch      Cost $3

         j + p = 5                      Multiply by -3              -3j  - 3p = -15

$2.50j + $3p = $14           Do not change      +   2.50j  -3p = 14      

                                                                                 - .50j      = -1

                                                                                          j = 2   Beetle Juice

   Substitute into the fist equation and solve for y       j + p = 5

                                                                                         2 + p = 5

                                                                                              p = 3   Potion Punch

Please help me y’all.

Answers

Step-by-step explanation:

6 > 4x - 5

Bringing like terms on one side

6 + 5 > 4x

11 > 4x

11/4 > x

Option none is the correct answer

Which variable is most important to the following problem?
A tentmaker has 60,000 tents in stock. The Army decides to order 350 tents
for each of its 200 brigades. Will the tentmaker have enough tents in stock?
O A. the price of one tent
O B. the number of tents the Army orders
C. the size of each tent

Answers

Answer:

B.) the number of tents the army orders

Step-by-step explanation:

The word problem does not speak of any prices or tent sizes so it cant be A or C

Answer:

its B

Step-by-step explanation:

What time is four past eight at night

Answers

Answer:

8:04 pm

Step-by-step explanation:

Answer:

8:04

Step-by-step explanation:

8 o'clock and four minutes past 8 is 8:04.

math
rate of change and show me how u did it:( <3

Answers

Answer:

y = m x + b   equation for a straight line

if x = o then y = 4 from graph

y = 0 + 4            and b = 4

If x = 8 then y = 24 from graph

24 = m * 8 + 4      substituting in our equation

m = 20 / 8 = 2.5      giving slope or rate of change

y = 2.5 x + 4     the final equation with a slope of 2.5

As a check using the graph:

We see that if y = 24 then x = 8

24 = m * 8 + 4      substituting in our equation

m = 20/8 = 2.5 agreeing with the value found

Will give brainliest

Answers

Slope equals rise over run

The distance of the points is 4 units down and 2 units right

-4/2 = -2

Slope = -2

Help for 100 points if correct

Answers

Total=2 1/4Used=3/8

Saved:-

[tex]\\ \sf\Rrightarrow 2\dfrac{1}{4}-\dfrac{3}{8}[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{9}{4}-\dfrac{3}{8}[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{18-3}{8}[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{15}{8}[/tex]

[tex]\\ \sf\Rrightarrow 1\dfrac{7}{8}[/tex]

Answer:

[tex]\textsf{D)} \quad 1 \dfrac{7}{8}[/tex]

Step-by-step explanation:

Subtract the used volume of punch from the starting volume of punch.

Convert the mixed number to an improper fraction:

[tex]\begin{aligned} \implies 2\frac{1}{4}-\frac{3}{8} & = \dfrac{2 \times 4+1}{4}-\dfrac{3}{8}\\\\ & = \dfrac{9}{4}-\dfrac{3}{8}\end{aligned}[/tex]

Make the denominators of both fractions the same by multiplying the numerator and the denominator of 9/4 by 2:

[tex]\implies \dfrac{9 \times 2}{4 \times 2}-\dfrac{3}{8} = \dfrac{18}{8}-\dfrac{3}{8}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}:[/tex]

[tex]\begin{aligned} \implies \dfrac{18}{8}-\dfrac{3}{8} & = \dfrac{18-3}{8}\\\\ & = \dfrac{15}{8}\end{aligned}[/tex]

Convert back into a mixed number:

[tex]\begin{aligned}\implies \dfrac{15}{8} & = \dfrac{8+7}{8}\\\\ & = \dfrac{8}{8}+\dfrac{7}{8}\\\\ & = 1\dfrac{7}{8}\end{aligned}[/tex]

PLZ HELP
Given the side lengths, determine whether the triangle is acute,right, obtuse, or not a triangle.
15,17,21
Not a triangle
A cute
Right
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3,9,10
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Acute
Right
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Answers

Answer:

It is an acute scalene triangle

Step-by-step explanation:

All angles are acute, making it an acute triangle

scalene because all sides are different lengths

If there are 42 boys and 54 girls in a room, fill out all of the possible ratios of boys to girls that could be made.

Answers

Answer:

42:54,54:42

Step-by-step explanation:

solve for x & y

plsssss, sorry.

Answers

Answer:

[tex]\huge\boxed{x=29;\ y=51}[/tex]

Step-by-step explanation:

This is Isosceles triangle (look at the picture).

We know:

All triangles have internal angles that add up to 180°

Therefore:

[tex](x-2)+(x-2)+(4x+10)=180[/tex]

combine like terms:

[tex](x+x+4x)+(-2-2+10)=180\\\\6x+6=180\qquad|\text{subtract 6 from both sides}\\\\6x=174\qquad|\text{divide both sides by 6}\\\\x=29[/tex]

(x - 2)° and 3y° are supplementary angle (Two Angles are Supplementary when they add up to 180°).

Therefore:

[tex]3y+(x-2)=180[/tex]

substitute x = 29 and solve for y:

[tex]3y+(29-2)=180\\\\3y+27=180\qquad|\text{subtract 27 from both sides}\\\\3y=153\qquad|\text{divide both sides by 3}\\\\y=51[/tex]

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Answers

Answer:

[tex]x^2 +6x +2=0[/tex]

Step-by-step explanation:

Y=-2|x+2|-4 i need to find y intercept and the x intercept

Answers

Answer:

x-int: ∅

y-int: (0,-8)

Step-by-step explanation:

To find the x and y-intercept, simply plug in zero for x and y:

[tex]0=-2|x+2|-4\\4=-2|x+2|\\-2=|x+2|\\[/tex]

Because an absolute value cannot be equal to a negative, there is no x-intercept.

[tex]y=-2|0+2|-4\\y=-2|2|-4\\y=-4-4\\y=-8[/tex]

Hope it helps :)

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Answers

X roughly equals 3.99

Help help help math math

Answers

Answer:

V = 500 cm³

Step-by-step explanation:

V = 4/3 πr³

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ben drives 1/4 mile in 2/3 hours. what is the rate at which he drives

Answers

Answer:

3/8 or 0.375mph.

Step-by-step explanation:

All you have to do for this is divide one fourth by two thirds. This way, you get the units to work out as well.

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CAN SOMEONE HELP ME PLEASE ASAP!?

Answers

Answer:

36.1 in.

Step-by-step explanation:

1:19 , 1.9in.

1.9 * 19

which equals 36.1 in.

(HOpe This hElps:)

If correct plz give brainliest ; )

What the person said just

HELP ME PLEASE GUYS!! :)

Answers

If two lines intersect, then there is only one solution - where they cross.

Looking at the graph, we can see the intersection point of these two lines.

The intersection point is (1,1) - one unit to the right of the origin and one unit up.

Hope this helps! :)

Which statement is true?


Which statement is true?


The equation -x2 + 6x + 9 = 0 has no real solutions


The equation -x2 + 6x - 9 = 0 has one real solution


The equation -x2 + 6x - 9 = 0 has two real solutions


The equation -x2 + 6x + 9 = 0 has three real solutions



Answers

Answer:

The equation -x2 + 6x - 9 = 0 has two real solutions.

Step-by-step explanation:

[tex] {b}^{2} - 4ac = {6}^{2} - 4( - 1)( - 9) = 0 [/tex]

The discriminant equals to 0, so the quadratic equation has 1 real solution.

help i dont know how to do this !!!!!!!!!!!! for brainlist

Answers

Answer:

We can simplify everything to the power of 2:

[tex]8^{x+2} = 2^{3*(x+2)}=2^{3x+6[/tex]

[tex]16^{x+1} = 2^{4*(x+1)}=2^{4x+4[/tex]

As the two equations are equal to each other and they have common bases, their powers must be equal too. We can come up with this equation:

3x+6=4x+4

solve for x

x=2

D (last answer choice)

plug x=2 in and check and you will get 4096=4096

For the function, f(x)=20x+135, what does x represent?

Answers

The answer is x= -25/4

Ashley is bagging 32 pumpkin mut
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will number
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Answers

Answer:

4 of each, 8 pumpkin bags, 7 banana bags

Step-by-step explanation:

4 is the GCF of 32 and 28.

Divide each number by 4

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Answers

8.722 / (-3.56)

Expand [tex]\frac{8.722}{-3.56}[/tex] by multiplying both numerator and denominator by 1000.

[tex]\frac{8722}{-3560}[/tex]

Reduce the fraction [tex]\frac{8722}{-3560}[/tex] to the lowest terms by extracting and cancelling out 178.

-[tex]\frac {49}{20}[/tex] = -2.45

HELP ASAP PLEASE?!

The graph at the right shows Jeremy's distance from home each hour he is on a car trip. How many miles will he be from home after 10 hours?

A) 350 miles
B) 400 miles
C) 500 miles
D) 550 miles

Answers

Answer:

The answer is (C) because every time the hour goes up, the mile goes up by 5 so if you continue to count up by 5's you would get 500 at 10.

mr polaski bought a variety pack of muffins that has 9 apple muffins. the ratio of apple muffins to blueberry muffins in variety pack is 3:5 . how many blueberry muffins are in ms polaski's variety pack?

Answers

Answer:

He has 15 Blueberry Muffins

Step-by-step explanation:

If the ratio is 3 to 5, and he has 9 apples, that means that he has 3 times the normal ratio. So, multiply 5 by 3 and you get 15 blueberries.

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