1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Artist 52 [7]
9 months ago
8

Hello,how do I calculate the the volume of this compound shape?

Mathematics
1 answer:
Setler [38]9 months ago
3 0

To calculate the volume, we can divide this figure into three shapes. Three rectangular prisms, like the following image

The volume of a rectangular prism is given by the product between its 3 different dimensions, width, length and height. The green prism is the easiest to see the its dimensions, it has a width equals to 3, a length equals to 3 and a height equal to 1/2, therefore, its volume is

V_g=3\times3\times\frac{1}{2}=9\times\frac{1}{2}=\frac{9}{2}=4\frac{1}{2}

Since the width of the green prism is 3 and the red prism is 1 1/2 apart from the corner of the green prism, the width of the red prism is the difference between those values.

3-1\frac{1}{2}=\frac{6}{2}-\frac{3}{2}=\frac{6-3}{2}=\frac{3}{2}=1\frac{1}{2}

The length and the height of the red prism are also easy to see on the image, both of those values are 1, which means the volume of the red prism is

V_r=1\frac{1}{2}\times1\times1=1\frac{1}{2}

Finally, the last prism is the blue prism. The height of the green prism and the blue prism combined is equal to 3/4. Since the height of the green prism is 1/2, the height of the blue prism is

\frac{3}{4}-\frac{1}{2}=\frac{3}{4}-\frac{2}{4}=\frac{3-2}{4}=\frac{1}{4}

The length of the red prism and the blue prism combined is equal to 3, since the length of the red prism is 1, the length of the blue prism is

3-1=2

The width of the blue prism is given, it is equal to 1. With those dimensions, we can finally calculate the volume of the blue prism.

V_b=\frac{1}{4}\times2\times1=\frac{1}{2}

The total volume of the compound shape is the sum of all those volumes we calculated.

V=V_g+V_r+V_b=4\frac{1}{2}+1\frac{1}{2}+\frac{1}{2}=6\frac{1}{2}

You might be interested in
These box plots show daily low temperatures for a sample of days in two different towns.
KengaRu [80]
B
Is the correct answer



8 0
3 years ago
Read 2 more answers
Find the x- and y-intercepts of the following equation:<br> 2x+3y=-24
Ilya [14]

Answer:

Algebra 

 Topics 

How do you find the intercepts of x2y−x2+4y=0?

Algebra  Graphs of Linear Equations and Functions  Intercepts by Substitution

2 Answers

Gió

Mar 24, 2015

For the intercepts you set alternately x=0 and y=0 in your function:

and graphically:

Answer link

Alan P.

Mar 24, 2015

On the X-axis y=0

So

x2y−x2+4y=0

becomes

x2(0)−x2+4(0)=0

→−x2=0

→x=0

On the Y-axis x=0

and the original equation

x2y−x2+4y=0

becomes

(0)2y−(0)2+4y=0

→y=0

The only intercept for the given equation occurs at (0,0)

Answer link

Related questions

What is the x and y Intercepts?

How many intercepts can a line have?

How do you use substitution to find intercepts?

How do you identify the intercepts on a linear graph?

How do you use the x and y intercepts to graph a linear equation?

How do you find the x and y intercept for y=2x+3?

How do you find the x intercept for y=2?

What is the y intercept for the y=2 graph?

What is the y intercept for x=−1?

How do you find the x-intercept of the line 

4 0
1 year ago
the providence children muesuem installed a fence around the perimeter of the propety. the propety is a rectangle. one side is 3
mash [69]
Its a rectangle so two sides are equal and both sides that are opposite of each other are equal. So two sides are 37. Then you add them together to get 74, then subtract it from 164 to get 90 the rest of the fence length. Then divide it by two to get 45 which is the other side lengths, so it would be a 37 by 45 rectangle one side would be 37 while the other two are 45.
7 0
3 years ago
Solve for R. 3 + 3r &gt; 9
Nostrana [21]

Answer:

r > 2

Step-by-step explanation:

9-3 = 6

6/3 = 2

Have a good day :)

7 0
3 years ago
Write down the value of 2 with the power of 3
beks73 [17]

Answer:8

Step-by-step explanation:2 x 2=4 x 2=8

6 0
3 years ago
Read 2 more answers
Other questions:
  • Jamal has $35 to spend at the mall. If pairs of shorts are $9.99, how many can he buy?
    11·2 answers
  • Please help me in anything you can please try to do both of them I really need the answer
    5·1 answer
  • Which of the following is the correct factorization of this trinomial?
    9·1 answer
  • Which situation is best modeled with a division expression?
    7·1 answer
  • If the height is 4.41 inches and the volume is 0.734, what will the side length of the pyramid’s base be? Is the number rational
    11·1 answer
  • How do you turn 1/2 to a decimal
    5·2 answers
  • A cone and a cylinder have the same height and their bases are congruent circles
    12·1 answer
  • Advance Algebra Logarithm Task
    9·1 answer
  • The operation * on the set Z of integers is defined by x*y = 3x + 2y - 1, x, y E Z. Find the value of x such that x*2=5​
    7·1 answer
  • Find the area of a circle with radius, r = 5.69m.<br> Give your answer rounded to 2 DP.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!