6.
Which expression represents the volume of the composite figure
formed by a hemisphere with radius r and a cube with side length 2r?

6.Which Expression Represents The Volume Of The Composite Figureformed By A Hemisphere With Radius R

Answers

Answer 1

Answer:

A. [tex]r^{3}[/tex]([tex]\frac{2}{3}[/tex][tex]\pi[/tex] + 8)

Step-by-step explanation:

A composite figure is formed by two or more shapes in contact.

Volume of a cube = [tex]l^{3}[/tex]

where l is the length of its sides.

Given that l = 2r, then;

volume of the cube = [tex](2r)^{3}[/tex]

                                 = 8[tex]r^{3}[/tex]

volume of the cube = 8[tex]r^{3}[/tex]

For a hemisphere, volume = [tex]\frac{2}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]

Also,

volume of the hemisphere = [tex]\frac{2}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]

So that,

volume of the composite figure = volume of the cube + volume of the hemisphere

                                                 = 8[tex]r^{3}[/tex] + [tex]\frac{2}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]

                                                 = [tex]r^{3}[/tex](8 +  [tex]\frac{2}{3}[/tex][tex]\pi[/tex])

volume of the composite figure =  [tex]r^{3}[/tex]([tex]\frac{2}{3}[/tex][tex]\pi[/tex] + 8)


Related Questions

Use the domain (1/2, 1, 2, 4, 8) to plot the points on the graph for the given equation. The grid marks represent one unit,
the horizontal red line represents the x-axis, and the vertical red line represents the y-axis.
y = log 2 x

Answers

According to values of a function we can plot the points on a graph.

What is domain?

Domain is the value which we used to enter in a function to get the value of a function.

How to plot the points on the graph?

We have been given the domain of the function and we have to plot the value in the graph.

F(1/2)=log1=0

F(1)=log2=0.3

F(2)=log4=0.6

F(4)=log8=0.9

F(8)=log16=1.2

Learn more about graphs at https://brainly.com/question/4025726

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Given that GJ=70.2, JH=26, and GK=70.2, find the measure of JK

Answers

Answer:

52

Step-by-step explanation:

The two sides (GJ and GK) are congruent, and the angle of ∠GHJ is 90°.

It means JH ≅ HK.

JH = 26 so you multiply 2.

26 x 2 = 52

JK = 52

The measure of the side JK is 52 units if the GJ=70.2, JH=26, and GK=70.2 after applying the Pythagoras theorem.

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

It is given that:

GJ=70.2, JH=26, and GK=70.2,

In the right angle triangle JHG:

GH = √(GJ² - JH²)

GH = √(70.2² - 26²)

GH = 65.20

Similarly, applying Pythagoras' theorem in the triangle GHK:

HK = √(GK² - GH²)

HK = √(70.2² - 65.20²)

HK = 26.01

JK = JH + HK

JK = 26 + 26.01

JK = 52.01 = 52

Thus, the measure of the side JK is 52 units if the GJ=70.2, JH=26, and GK=70.2 after applying the Pythagoras theorem.

Learn more about the right-angle triangle here:

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giving points and brainly

Answers

Answer:

A 159.25 to the second power

Step-by-step explanation:

he simplest (and most commonly used) area calculations are for squares and rectangles. To find the area of a rectangle, multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.

what are the like terms in these?


3+5y-2g+7y


9g+5-2g+8x

Answers

Answer:

so the first one is 3+12y−2g

and the second one is 7g+5+8x

Step-by-step explanation:

im rlly rlly sorry if its wrong !!

A bag has one red ball, three blue balls and twice as many green balls as blue balls. if one ball is drawn (without looking) from the bag what are the chances that the ball will be blue?

Answers

Answer:

3/10 or three tenths or 0.3 or 0.30

Step-by-step explanation:

Plz brainliest

Answer: 30% or 3/10

Step-by-step explanation:

First you need to figure out how many balls are in the bag. There is 1 red, 3 blue, and 2x (x=# of blue balls) green balls. since there is 3 blue balls you double 3 to get how many green balls there are, which is 6. Then you do 1+3+6 to give you 10. Since there is 3 blue balls in a bag that consists of 10 balls, you have a probability of 3/10 or 30% or .3 to draw a blue ball.

3x2+2
-5x - 4
2x - 7
-2x2+10
Hint: To find the perimeter of a polygon, add all the sides

Answers

Answer:

The perimeter of a 4-sided polygon: P = x²-3x+1

Step-by-step explanation:

Given the lengths of the sides of a given polygon

3x²+2-2x²+102x-7-5x-4

The perimeter of a 4-sided polygon can be determined by adding the lengths of all 4 sides.

Perimeter = (3x²+2) + (-2x²+10) + (2x-7) + (-5x-4)

Remove the parentheses

                =3x²+2-2x²+10+2x-7-5x-4

Group like terms

                =3x²-2x²+2x-5x+2+10-7-4

Add similar elements:   3x²-2x²=x²

                 =x²+2x-5x+2+10-7-4

Add similar elements:   2x-5x=-3x

                 =x²-3x+2+10-7-4

                 =x²-3x+1

Therefore, the perimeter of a 4-sided polygon: P = x²-3x+1

Please help ASAP Tysm guys!

Answers

Answer:

it would be 3

Step-by-step explanation:

theeeeee answerrrrrr is 9

The measures of the angles of A ABC are given by the expressions in the table.
Angle
Measure
A
(4x – 13)
B
15
С
(x +18)
What is the measure of ZA and ZC?
Enter your answers in the boxes
mZA =D
mZC=

Answers

Answer:

m∠A = 115°

m∠C = 50°

Step-by-step explanation:

By triangle sum theorem,

Sum of measures of all interior angles of a triangles equals to 180°.

m∠A + m∠B + m∠C = 180°

By substituting the values of the angles from the given table,

(4x - 13) + 15 + (x + 18) = 180

(4x + x) + (-13 + 15 + 18) = 180

5x + 20 = 180

5x = 180 - 20

x = [tex]\frac{160}{5}[/tex]

x = 32

m∠A = (4x - 13)° = 4(32) - 13

                          = 115°

m∠C = (x + 18)° = 32 + 18

                         = 50°

Based on the properties of the internal angles in triangles, the measure of the angles A and C from the triangle ABC are equal to 115° and 50°, respectively. #SPJ5

What are the measures of the internal angles of the triangle ABC?

According to geometry, triangles are figures formed by three sides and three internal angles and, likewise, the sum of the measures of the internal angles equals 180°. Based on the latter property, we should solve the following expression for x:

(4 · x - 13) + 15 + (x + 18) = 180

5 · x + 20 = 180

5 · x = 160

x = 32

Finally, the measure of the angles A and C from the triangle ABC are, respectively:

m ∠ A = 4 · 32 - 13 = 115°

m ∠ C = 32 + 18 = 50°

Based on the properties of the internal angles in triangles, the measure of the angles A and C from the triangle ABC are equal to 115° and 50°, respectively. #SPJ5

To learn more about triangles, we kindly invite to check this verified question: https://brainly.com/question/2773823 #SPJ5

#21 pls help!!!!! would greatly be appreciated

Answers

I’m pretty sure A is the right answer




Uhmmm what they said ^

Which value of n makes the equation true?
1/2(n+4)=6

Answers

Answer:

8

Step-by-step explanation:

1/2(12)=6

Answer:

8

Step-by-step explanation:

1/2(8+4)=6

A sphere has a Volume of 972 cubic feet. Find the radius of the sphere.

Answers

Answer:

6.15

Step-by-step explanation:

6.15 is the answer that is it

Use the linear combination method to solve this system of equations. What is the value of x? 3 x + 7 y = 31. Minus 3 x minus 2 y = negative 1 Negative 6 Negative 3 and two-thirds 3 and two-thirds 6

Answers

Answer:

x = -3 2/3

Step-by-step explanation:

Given the simultaneous equations;

3 x + 7 y = 31 ..... 1

-3x - 2y = -1 ..... 2

Add both expressions

7y - 2y = 31-1

5y = 30

y = 30/5

y = 6

Substitute y = 6 into equation 2

From 2;

-3x - 2y = -1

-3x - 2(6) = -1

-3x - 12 = -1

-3x  = -1  + 12

-3x  = 11

x = -11/3

x = -3 2/3

Hence the value of x is -3 2/3

Answer:

x = -3 2/3

Step-by-step explanation:

Mindy needs to rake a rectangular part of her yard that is 9 feet by 8 feet. It takes her 10 minutes to rake an area that is 12 feet square. How long will it take Mindy to rake the rectangular part of her yard?

Answers

Answer:

60 minutes

Step-by-step explanation:

Time taken to rake 12ft² = 10 minutes

Area of Mindy's rectangular path :

Area of rectangle = Length * Width

Dimension of Mindy's rectangular path = 9ft by 8ft

Area = 9ft * 8ft

Area = 72ft²

Hence, it will take Mindy;

(Area of Mindy's path / 12 ft) * time taken

(72ft² / 12ft²) * 10 minutes

6 * 10 = 60 minutes

1/9x=5
solve for x
please show step by step

Answers

Answer:

x=1/45

Step-by-step explanation:

do the inverse

please mark it as brainliest!!<3

Find the prime factorization of 120.


23 × 3 × 5

2 × 32 × 5

2 × 3 × 5

2 × 32 × 52

Answers

Answer:

(7/8 - 4/5)^2 = 9/

1600

= 0.005625

Step-by-step explanation:

Subtract: 7/

8

- 4/

5

= 7 · 5/

8 · 5

- 4 · 8/

5 · 8

= 35/

40

- 32/

40

= 35 - 32/

40

= 3/

40

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(8, 5) = 40. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 5 = 40. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - seven eighths minus four-fifths = three fortieths.

Exponentiation: the result of step No. 1 ^ 2 = 3/

40

^ 2 = 32/

402

= 9/

1600

In words - three-fortieths squared = nine one-thousand six-hundredths.

help me with this thanks for anyone who helps! :D

Answers

Answer:

x= 90-60

x=30

Step-by-step explanation:

Answer:

30° is the answer because its a right angle

Step-by-step explanation:

can you mark me brainliest? thank you

The temperature was 75° Fahrenheit. The temperature dropped at a rate of 10° per hour.
What was the temperature in degrees 8 hours later?

Answers

Answer:

-5 degrees

Step-by-step explanation:

you started at 75 degrees. it dropped at a rate of 10 degrees per hour. It's been eight hours. 8 times 10 equals 80. It dropped a total of 80 degrees. the starting 75 degrees minus the current 80 degrees equals -5 degrees.

At a dinner, the meal cost $22 and a sales tax of $1.87 was added to the bill. At the same restaurant, another family had a meal and the meal cost $66.00. How much would the sales tax be on a $66 meal?

Answers

Answer:

71.61

Step-by-step explanation:

hope this helps good luck

Factor this trinomial.
x² + 3x - 4
A. (x-4)(x-1)
B. (x - 4)(x + 1)
C. (x + 4)(x + 1)
D. (x+4)(x - 1)

Answers

The answer is the d i hope is help you

Answer:

(x-1)(x+4), so D.

Step-by-step explanation:

(r - 3)(3r + 6)= ? .....

Answers

r(3r+6)-3(3r+6)
3r² +6r-9r-18
3r²-3r-18

what is equivalent to 8+3•12​

Answers

Answer:

Step-by-step explanation:

There are infinity equivalent fractions to 812. See some examples: 23, 46, 69, 812, 1015, 1218, 1421, 1624, 1827, 2030, 2233, 2436, 2639, 2842, 3045, 3248, 3451, 3654, 3857, 4060...

3.
If the volume of cylinder of height 7 cm is 448 cm², then the total surface area of cylinder is
(1) 2041 cm?
(2) 2241 cm?
(3) 2481 cm?
(4) 240 cm?

Answers

Answer:

A = 240π cm²

Step-by-step explanation:

Given that,

Height of a cylinder, h = 7 cm

Volume of the cylinder, V = 448π cm³

We need to find the total surface area of the cylinder.

The formula for the volume of the cylinder is given by :

[tex]V=\pi r^2 h\\\\r=\sqrt{\dfrac{V\pi }{\pi h}} \\\\r=\sqrt{\dfrac{448\pi }{\pi \times 7}} \\\\r=8\ cm[/tex]

The formula for the total surface area of the cylinder is given by :

[tex]A=2\pi r(r+h)\\\\A=2\pi \times 8\times (8+7)\\\\A=240\pi \ cm^2[/tex]

So, the total surface area of the cylinder is 240π cm².

Graph the line that passes through the points (2,8) and (-5,8) and determine the equation of the line.

Answers

Answer: y=7

Step-by-step explanation:

First, graph the points, and you get a horizontal line. You see that the line is on the Y-Axis, and hits the y-axis at (0,7). Since it is horizontal, you get y=7

Anne is playing golf. On the first tee, she hits a slow shot down the Y = x -0.0 4X squared, we are why is the balls hide in the air and eggs is a horizontal distance in his drawer from the tea. The distance or measured in feet how far from the tea does the ball hit the ground

Answers

Answer:

25 ft

Step-by-step explanation:

The path of the golf ball is given by the equation.

[tex]y=x-0.04x^2[/tex]

The point on the ground where the ball will land on the ground is the point where [tex]y=0[/tex].

[tex]x[/tex] is horizontal distance

So

[tex]0=x-0.04x^2\\\Rightarrow x(1-0.04x)=0\\\Rightarrow 1-0.04x=0\\\Rightarrow x=\dfrac{1}{0.04}\\\Rightarrow x=25[/tex]

So, the ball will land 25 ft away from the tee.

For each graph shown below, select the correct description for slope and y-intercept. In the fourth column, create an equation that can be used to describe the function shown in the graph.

Answers

Answer is B I’m sure

Jill bought a lamp for $40. She sold it at a garage sale for $12. What was the approximate decrease?

Answers

Answer:

she was left with 28$ I'm in high school i think I'm right

Step-by-step explanation:

Need help i suck at mathh

Answers

the answers is $2 more than Marc

Multiply (x+2)(x2−3x +4)

2x2−6x+8

x3+5x2+10x+8

x2−2x+6

x3−x2−2x+8
Plz help i mark brainliest

Answers

Step-by-step explanation:

Using FOIL, we have

(x + 2)(x² - 3x + 4)

= (x³ - 3x² + 4x) + (2x² - 6x + 8)

= x³ - x² - 2x + 8.


g(x) = 4f(x)

Is this a vertical or a horizontal translation

Answers

Answer:

this is a vertical

Step-by-step explanation:

Please help as soon as possible

Answers

Answer:

Step-by-step explanation:

the answer is No its not similar

because the factors don't work

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