# area

1. ### Surface Area of a Regular Tetrahedron

How to find the surface area of a regular tetrahedron using calculus? The surface area should be √3 a^2. I tried to do the same approach that MarkFL did for the volume but I could not figure out how to do it with the area!
2. ### Calculate volume of irregular triangular pyramid using differences between prisms

Here's a picture to better depict what I'm talking about: The red shape is the irregular triangular pyramid, the blue shape is the triangular prism. All vertices of the pyramid have different z-values (except the ones shared with the prism). I could of course calculate the volume of the...
3. ### Finding the area and volume of a region bounded by two curves

Hi all, I am a bit confused as to how to find the region R bounded by two graphs. The specific problem is: The region R shown is bounded by the graphs of y=2^-x and y=2cos(x). a) Find the area of R b) Determine the volume of the solid generated by revolving R about the line y=3 c) Determine...
4. ### Math 111 College Algebra-Expressing the area of a right triangle.

The vertices of a right triangle in the first quadrant are (0, n), (0,0) and (k, 0). Draw a picture that represents the situation described. If the hypotenuse passes trough the point (5,2), express the area of the triangle in terms of k. Please explain how you got your answer, this is the...
5. ### Area of a Parallelogram

I have to find the area of this parallelogram, but the only three things I'm told are that AD = 5, EF = 11, and EFC = 90º. So far I've tried using the pythagoras theorem, and the special 30-60-90 triangle theorem (longer cathet = √3 * shorter cather OR (√3/2) * Hypotenuse), but they all lead to...
6. ### Riemann Sum for 1/x

How to find the integral 1/x from 1 to 2 using riemann sum? ∫ 1/x dx = lim as n goes infinity Σ(i = 1 to n)f(xi)Δx Δx = 2-1/n = 1/n xi = 1 + iΔx = 1 + (i/n) = lim as n goes infinity Σ(i = 1 to n)f(1 + (i/n))(1/n) = lim as n goes infinity Σ(i = 1 to n)[ 1 / (1 + (i/n)) ] (1/n) = lim as n goes...
7. ### area bounded by (y^2) + (x-2)^2 = 4 and y = x in first quadrant

Evaluate ydA where R is region between (y^2) + (x-2)^2 = 4 and y = x in first quadrant ...My ans is 32/3 , but given ans is 4/3.. What's wrong with my working?
8. ### Surface area over y-axis (integrating wrong)

The book says the answer is 15\pi\sqrt{17} I have tried to manipulate the numbers to try to get that answer, but I don't know what mistake(s) I am doing.
9. ### prove surface area of sphere

I 'm having problem of proving the total surface area of sphere = 4pi(a^2) , in my workin g, i got surface area = 2pi(a^2) only .... I 've checked it many times , still cant figure out which part i'm wrong... P/s : the sphere has radius of a .
10. ### area of region outside the circle by r =1 and inside the cardroid r = 1- sin (theta)

Find the area of region outside the circle by r =1 and inside the cardroid r = 1- sin (theta) Here's my working. but the ans given is 2 + (pi/4) unit ... Why am i wrong ?
11. ### area bounded by ∫∫ sin(theta)dA

Evaluate area bounded by ∫∫ sin(theta)dA , where R is the region outside circle r =2 and inside cardroid r = 2 + 2 cos(theta) , in first octant .... I have sketched the area , is it correct ? The ans provided is 4/3 , however i gt 2 . Which part is wrong ?
12. ### double integral of surface area

By using double integral , find the surface area of the portion of plane x +y =z = 3 that lies above disc (x^2) + (y^2) < 2 in first octant… Why shoudnt the surface area be the whole red area + the black area ? Since it’s say lies above disc (x^2) + (y^2) < 2 …Btw, the x^2) + (y^2) < 2 means...
13. ### double integral to find area

find ∫∫ y dA , where R is the region between (y^2) + (x-2)^2 = 4 and y = x in the first quadrant i have skteched out the diagram and did it,. But my ans is 13/ 3 rather than 4/3 , is the ans provided wrong ? P/s : ans provided is 4/3 ...
14. ### Maximizing the area of a window

Does anyone know how to work this out. Any help much appreciated. it is question 32 i'm stuck on
15. ### triangle area

I was sure i did this correctly but the answer is totally different and i cant figure why Lines K and L intersect at the point P (b) calculate coordinates of P (i did that using simultaneous equations) Line L y=2x-15 Line K y=-1/2x O(0,0) C(0,-15) P(6,-3) (c) given that line L crosses y-axis...
16. ### Surface Area of Revolution

Compute the surface area of revolution of f(x) = 2/3(1+x^2)^(3/2) about the x-axis over the interval [0,3]. Integral [0,3] 2piy sqrt(x+2) = 4/3(5sqrt5-2sqrt2)pi???
17. ### double integral (surface area)

I have 2 formula to find area here , the first formula is restricted to 2d plane only ? While in the second note , the formula is for 3d plane ? so , the surface area is the total surface area of all 2d plane? or surface area in the specific plane only ?
18. ### line integral vs surface area integral

in part b , we can find mass by density x area ? is it because of the thin plate, so, the thickness of plate can be ignored?
19. ### Determine the area in sq ft of a yard, only knowing the distance around it

Hello all, This particular problem is a practical problem I have. The shape of my yard is not a perfect cylinder. If you were to fly over it at a low altitude it would look like a beaker that has it's funnel glass bent to the right. So, it definitely looks like a beaker with the base of the...
20. ### finding surface area using projection of plane

by using double integrals , find the surface area (x^2) +(y^2) +(z^2) =4 that lies between plane z =1 and xy -plane why the surface area is only the ring part where the limit is sqrt rt 3 to 2 , why not the whole thong , namely from 0 to 2 ? (refer to the projection region on xy-plane)