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
157×23 show work pls​
Sergeeva-Olga [200]

Step-by-step explanation:

  • 157×23
  • 3611

hope it helps

<h3>stay safe healthy and happy.</h3>
8 0
3 years ago
Read 2 more answers
A geometry teacher asked Radric to define "parallel lines." Radric said that parallel lines are lines in a plane that do not hav
UkoKoshka [18]

Answer: The answer is Yes.

Step-by-step explanation:  Given in the question that Radric was asked to define "parallel lines" and he said that parallel lines are lines in a plane that do not have any points in common. We are to decide whether Radric's definition is valid or not.

Parallel lines are defined as lines in a plane which never meets or any two lines in a plane which do not intersect each other at any point are called parallel.

Thus, Radric's definition is valid.

6 0
3 years ago
Read 2 more answers
Will bought 3 college textbooks. One cost $32, one cost $45, and one cost $39. What is the average price of his books? Choose th
Snowcat [4.5K]
D. Since you bought 3 text books you will have to multiply and then add the rest of the numbers
3 0
3 years ago
Read 2 more answers
A student on a piano stool rotates freely with an angular speed of 2.85 rev/s . The student holds a 1.50 kg mass in each outstre
Vlad1618 [11]

Answer:r'=0.327 m

Step-by-step explanation:

Given

N=2.85 rev/s

angular velocity \omega =2\pi N=17.90 rad/s

mass of objects m=1.5 kg

distance of objects from stool r_1=0.789 m

Combined moment of inertia of stool and student =5.53 kg.m^2

Now student pull off his hands so as to increase its speed to 3.60 rev/s

\omega _2=2\pi N_2

\omega _2=2\pi 3.6=22.62 rad/s

Initial moment of inertia of two masses I_0=2mr_^2

I_0=2\times 1.5\times (0.789)^2=1.867

After Pulling off hands so that r' is the distance of masses from stool

I_0'=2\times 1.5\times (r')^2

Conserving angular momentum

I_1\omega =I_2\omega _2

(5.53+1.867)\cdot 17.90=(5.53+I_o')\cdot 22.62

I_0'=1.397\times 0.791

I_0'=5.851

5.53+2\times 1.5\times (r')^2=5.851

2\times 1.5\times (r')^2=0.321

r'^2=0.107009

r'=0.327 m

7 0
3 years ago
SOLVE
Varvara68 [4.7K]

Answer:

26.4 is what i came up with if you divide im probably wrong sorry if i am

5 0
3 years ago
Other questions:
  • Circle which of the following are
    15·1 answer
  • What is the vertex of the following graph?
    8·1 answer
  • ‘write an equation of the line that passes through each pair of points’ (1,2) and (4,8)
    10·1 answer
  • What is the vertex and x intercepts of y=x^2-2x-35 Just answers pls :)
    14·1 answer
  • The highest point over the entire domain of a function or relation
    8·1 answer
  • What are the vertex and x-intercepts of the graph of the function given below?<br> y = x^2 - 2x - 48
    14·2 answers
  • Please help me on this question. I forgot how to do it​
    9·1 answer
  • 3(x + 10) + 6 = 3(x + 12)
    5·2 answers
  • What would be another way to write -8n-7
    7·1 answer
  • Simplify each of the expression (x-7)(x+3)
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!