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
Mark has a piece of wood 4 1/4 feet long. Tony has a piece of wood 1 2/4 feet long. How much wood do the boys have altogether. p
Alona [7]
They have 5 3/4 ft

4+1=5
1/4+2/4=3/4


but hey, its not the length of your wood that matters, its how you use it XD
8 0
3 years ago
Christian was 145 cm tall when he was 12 years old. And 3 years later, he became 168.2 cm tall. By what percent did Christian's
Sav [38]

Answer: 16%

Step-by-step explanation:

168.2 - 145 = 23.2

23.2/145 = 0.16

0.16 as a percent is 16%

6 0
3 years ago
Find the value of x and y in the parallelogram below.
Delicious77 [7]
In a parallelogram, the opposite angles are equal and the sum of the angles is 360 degrees.

W = Z and Y = X
3y = 3x
Y = X = y
3y + y + 3x + x = 360
3x + x + 3x + x = 360
8x = 360
x = 360/8 = 45

Therefore, x = 45; y = 45
7 0
3 years ago
HELP NOW IS THIS CORRECT
Arisa [49]
Yes this question is correct
4 0
3 years ago
In 2007 the population of the town of Cartersville was 24,455. The population growth can be represented by the formula P = 24,45
Triss [41]
P = 24455 (1.03)x
30,000/24455 (1.03) < x
The year must be > 1.19 + 2007, or 2008.19, which means in 2009, or in 2008 + 3 months
3 0
3 years ago
Other questions:
  • Let f(x) = 2x; its inverse is f1(x) = log2x. If f(5) = 32, what is f-1(32)?
    10·1 answer
  • Find The T value for point that splits segment EF in half if point E is located at (5,-2) and point F is located at (-1,3).
    9·1 answer
  • Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps
    15·1 answer
  • Can anybody help me answer this ASAP thank you
    7·1 answer
  • Find the surface area of the regular pyramid
    7·1 answer
  • Find the critical value ze necessary to form a confidence interval at the level of confidence shown below
    10·1 answer
  • 3.f(-4)-3.g(-2) please help me with this problem
    8·1 answer
  • Help plz dis is a lil importatnete
    9·2 answers
  • If a quadratic equation is given to you in vertex form, what is the vertex?
    12·2 answers
  • A baker bakes 50 muffins. 1/5 of the muffins are chocolate chip. 1/2 of the muffins are blueberry. The rest are cinnamon. How ma
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!