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
padilas [110]
2 years ago
12

Find the volume and area for the objects shown and answer Question

Mathematics
1 answer:
klio [65]2 years ago
6 0

Step-by-step explanation:

You must write formulas regarding the volume and surface area of ​​the given solids.

\bold{\#1\ Rectangular\ prism:}\\\\V=lwh\\SA=2lw+2lh+2wh=2(lw+lh+wh)\\\\\bold{\#2\ Cylinder:}\\\\V=\pi r^2h\\SA=2\pi r^2+2\pi rh=2\pir(r+h)\\\\\bold{\#3\ Sphere:}\\\\V=\dfrac{4}{3}\pi r^3\\SA=4\pi r^2

\bold{\#4\ Cone:}\\\\V=\dfrac{1}{3}\pi r^2h\\\\\text{we need calculate the length of a slant length}\ l\\\text{use the Pythagorean theorem:}\\\\l^2=r^2+h^2\to l=\sqrt{r^2+h^2}\\\\SA=\pi r^2+\pi rl=\pi r^2+\pi r\sqrt{r^2+h^2}=\pi r(r+\sqrt{r^2+h^2})\\\\\bold{\#5\ Rectangular\ Pyramid:}\\\\V=\dfrac{1}{3}lwh\\\\

\\\text{we need to calculate the height of two different side walls}\ h_1\ \text{and}\ h_2\\\text{use the Pythagorean theorem:}\\\\h_1^2=\left(\dfrac{l}{2}\right)^2+h^2\to h_1=\sqrt{\left(\dfrac{l}{2}\right)^2+h^2}=\sqrt{\dfrac{l^2}{4}+h^2}=\sqrt{\dfrac{l^2}{4}+\dfrac{4h^2}{4}}\\\\h_1=\sqrt{\dfrac{l^2+4h^2}{4}}=\dfrac{\sqrt{l^2+4h^2}}{\sqrt4}=\dfrac{\sqrt{l^2+4h^2}}{2}

\\\\h_2^2=\left(\dfrac{w}{2}\right)^2+h^2\to h_2=\sqrt{\left(\dfrac{w}{2}\right)^2+h^2}=\sqrt{\dfrac{w^2}{4}+h^2}=\sqrt{\dfrac{w^2}{4}+\dfrac{4h^2}{4}}\\\\h_2=\sqrt{\dfrac{w^2+4h^2}{4}}=\dfrac{\sqrt{w^2+4h^2}}{\sqrt4}=\dfrac{\sqrt{w^2+4h^2}}{2}

SA=lw+2\cdot\dfrac{lh_1}{2}+2\cdot\dfrac{wh_2}{2}\\\\SA=lw+2\!\!\!\!\diagup\cdot\dfrac{l\cdot\frac{\sqrt{l^2+4h^2}}{2}}{2\!\!\!\!\diagup}+2\!\!\!\!\diagup\cdot\dfrac{w\cdot\frac{\sqrt{w^2+4h^2}}{2}}{2\!\!\!\!\diagup}\\\\SA=lw+\dfrac{l\sqrt{l^2+4h^2}}{2}+\dfrac{w\sqrt{w^2+4h^2}}{2}\\\\SA=\dfrac{2lw}{2}+\dfrac{l\sqrt{l^2+4h^2}}{2}+\dfrac{w\sqrt{w^2+4h^2}}{2}\\\\SA=\dfrac{2lw+l\sqrt{l^2+4h^2}+w\sqrt{w^2+4h^2}}{2}

You might be interested in
Prove that sin(n) diverges
Ivahew [28]
If you look at the graph of sin(n), you can notice that it oscillates every kpi/2 when k is odd. This oscillation proves that sin(n) diverges.
8 0
3 years ago
Solve -2 = 5p + 3p -8 – 6p
Shalnov [3]

Answer:

P=3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−2=5p+3p−8−6p

−2=5p+3p+−8+−6p

−2=(5p+3p+−6p)+(−8)(Combine Like Terms)

−2=2p+−8

−2=2p−8

Step 2: Flip the equation.

2p−8=−2

Step 3: Add 8 to both sides.

2p−8+8=−2+8

2p=6

Step 4: Divide both sides by 2.

2p2=62

p=3

3 0
2 years ago
yall im timed please help! ill give you 20 more points when I'm done with my test and you get it correct
taurus [48]
I think it’s linear
4 0
3 years ago
Read 2 more answers
Mrs. Garcia used 5 cups of flour to make 3 loaves of bread. How many loaves of bread can she make with 30 cups of flour?
pochemuha
Well first you would do 5 / 30 which makes 6 then you would 6 times 3 equals 18. So she would make 18 loaves of bread. 
3 0
2 years ago
Solve this equation:<br><br> 110 = 9x + 5y<br><br><br> Help please!!!❤️
Archy [21]

We can't find explicit values for x and y, since there is only one equation, but two variables.


The best we can do is solve for one variable with respect to the other:


Solve for x:


subtract 5y from both sides:


110-5y = 9x


divide both sides by 9:


\frac{110-5y}{9} = x


Solve for y:


subtract 9x from both sides:


110-9x = 5y


divide both sides by 5:


\frac{110-9x}{5} = y



5 0
2 years ago
Other questions:
  • Freya is training for a track race. She starts by sprinting 200 yards. She gradually increases her distance, adding 5 yards a da
    5·3 answers
  • Ken can walk 40 dogs in 8 hours.<br> How many dogs can Ken walk in 12 hours?
    14·1 answer
  • Find the inverse of y = 3x+9
    11·2 answers
  • Which set of coordinates is a solution of the inequality, y&lt;2
    15·1 answer
  • What is the surface area of this solid
    10·1 answer
  • A pair of obtuse angles can also be vertical true or false
    13·1 answer
  • how can you copy a angle using a straightedge, a compass, and a pencil, give step by step instructions
    12·2 answers
  • Please only answer this with actual answers and ill give the award
    5·1 answer
  • Please answer correctly !!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!
    12·1 answer
  • Please answer below :-)
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!