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]
3 years ago
12

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

Mathematics
1 answer:
klio [65]3 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
A spherical tank has a capacity of 800 gallons. Using the fact that 1 gallon is about 0.1337 ft3, find the radius of the tank (t
nydimaria [60]

Solution-

Capacity of the spherical tank = 800 gallons.

1 gallon = 0.1337 ft³,

Volume of 800 gallons = 800 × 0.1337 = 106.96 ft³

Formula for the volume of sphere

V =\frac{4\pi r^{3}}{3}

Equating both the volumes

⇒ \frac{4\pi r^{3}}{3} = 106.96

⇒ r^{3} = 25.53

⇒ r = \sqrt[3]{25.53}

⇒ r = 2.94

∴ Radius of the sphere is 2.94 ft


6 0
3 years ago
Describe how you determined which fraction were already in the simplest form
MatroZZZ [7]
If the numerator and the denominator do not have a greatest common factor then the faction is in simplest form
7 0
3 years ago
I do need help please. Just number 14 :)
Ainat [17]
The difference between the coat cost for Delaware vs Fairfield is $0.60

Explanation:
For Delaware: 80 × .0725 = $5.80
80+5.80= $85.80

For Fairfield: 80 × .065 = $5.20
80+5.20=$85.20

85.80-85.20=0.60
7 0
3 years ago
Read 2 more answers
Split 840 into the ratio 2:5
pishuonlain [190]

Answer:

numbers are 3x,2x,5x

so 3x+2x+5x=10x=840

so x=84

so numbers are 252,168,420

7 0
2 years ago
BASKETBALL After Game 1, Felicia had scored 14 points. After Game 5, she had scored a total of 82 points for the season. After G
Stella [2.4K]

Let  p represents the number of points scored in n number of games.

So, the graph, the number of games, n is on the horizontal axis and the points scored, p, is on the vertical axis.

After Game 1, the point scored is 14,

so, the first point, P_1, on the graph is

P_1=(1,14)

After Game 5, the point scored is 82,

so, the second point, P_2, on the graph is

P_2=(5,82).

After Game 10, the point scored is 129,

so, the second point, P_2, on the graph is

P_2=(10,129)

First, represent all the three points, P_1, P_2 and P_3, on the graph, then connect P_1- P_2 and P_2 - P_3 as shown in the figure.

4 0
3 years ago
Other questions:
  • Question 20 please?
    15·1 answer
  • If you have a cat what is it name
    13·2 answers
  • Researchers wanted to determine if there was an association between the level of happiness happiness of an individual and their
    12·1 answer
  • Determine the number of solutions that exist to the equation below 8(j-4)=2(4j-16)
    13·1 answer
  • Find an equation of the line that satisfies the given conditions.<br> Through ​(0.4​,0.2); vertical
    13·1 answer
  • I need help <br> 5times 10 +25-9+2times2
    5·2 answers
  • Write an expression in the factored form that represents the area of the border?​
    13·1 answer
  • <img src="https://tex.z-dn.net/?f=%5Cfrac%7B350m%7D%7B1s%7D" id="TexFormula1" title="\frac{350m}{1s}" alt="\frac{350m}{1s}" alig
    10·1 answer
  • What is the answer for 7-2x=2(x-4)-1
    5·2 answers
  • Which graph represents the function p(x) = |x - 1|
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!