Volumes & Surface Area ?'s?

Question

a. A closed rectangular box has length of 3 inch, width 7 inches, and height of 3 inches.
The surface area is? Also what formula should I use?

b. An closed circular cylinder has radius 3 inches and height 6 inches. the area of the base is 9 (pi) square inches. the volume is how many cubic inches? (using A = pi r2)

c. a circular cone has a radius of 3 inches and height of 6 inches its volume is how many cubic (pi) inches?

Thank you thank you thank you!!!!

Answer 1

a) SA = 2*l*w + 2*w*h + 2*l*h

b) V = pi*r^2*h <--- volume of cylinder

c) V = (pi*r^2*h)/3 <---volume of a cone
Now all you have to do is sub in the appropriate numbers and voila!
I hope this helped :)

Answer 2

total surface area of a rectangular parallelopoid is given by the formula=2
(length*width+length*height+
width*height Therefore the surface area here
=2(3*7+3*3+3*7)
=2(21+9+21)
=2*51=102 sq.inch
2.It will be A*h
The complete formula for the volume of a circular cylinder is pi*r^2*h
3The volume of a circular cone is exactly one-third of a circular cylinder
It is 1/3 multiplied by pi*r^2*h or you may say pi*r^2*h divided by 3.
so the answer to your problem would be
pi*3^2*6/3
=3.14*9*6/3
=56.52 cubic inches

Answer 3

a. length X width X height = volume of a square or rectangle (and parrallelogram sp??) the answer is
3"x7"x3" = 63"
21" x 3" = 63"
9"x7" = 63"

b.correct. finish the math. r = 3", h=6".
The formula is pi*r^2 x h.
The formula looks like pi x 3^2" x 6" = volume
pi=3.1415 so... 3.1415 x 3^2" x 6" = volume
3.1415 x 9"x6 = 169.641 cubic inches

c. i don't remember the formula for a cone, but the answer is 56.5487 cubic inches

Answer 4

That would be the heaviest solids if weight and shape were the identity characteristics. Take 2 objects of identical weight and shape. The densest one, such as plutonium would have least volume. Quite recently 2 new elements have been discovered at Berkeley - 116 and 118 (identified by their number of protons). But if you are looking for a shapewise answer then it would be a flat sheet. The flatter, the better to fulfill your requirement to minimize volume to surface. And I claim it would not matter what 2 dimensional shape it took so long as it was flat. As a thought experiment, imagine that an object could be flattened down to 1 molecule thick. You would have all molecules exposed and the area would be the area of 1 molecule times the number of molecules in the object. So the 2 dimensional shape would not matter. Flatness is the key.

Answer 5

Volume of a cone = 1/3(Area of Base)(height) = 1/3 π r^2 h

Volume of a cylinder = π r^2 h

where '^' indicates "raise to the power of," so

Cone => 1/3 x 9 x 6 x π => 18π cubic inches
Cylinder => (3 x 3) x 6 x π => 54π cubic inches

Answer 6

a. The box has 6 sides. You can pair them up into 3
pairs (top and bottom, left and right, front and back)
If l is length, w is width, h is height, the formula is
2lw + 2lh + 2wh. You can do the math

b. for a cylinder, volume = (pi r2)h or 9(pi)*6 = 54(pi) sq in

c. for a cone, volume = 1/3(pi r2)h. The answer is 1/3 of what
you got for b.

Answer 7

Surface area is all of your bases added together,so for a box it would be the length times the height times 2 because you have two of them added with 2 times your length times your width and that added to your height times your width. So it is 2{ (3*7)+(3*3)+(3*3)}=SA.. just factored the two out. Don't use a formula think of it as adding all the areas you have together, so you have three different sides which are areas that you just have to times together to get the area because they are squares.

Volume is base times height. Your base is a circle. Find the area of your base times your height and you have your answer to b.

Same for the third one.

Volume is always area of your base times your height.

Answer 8

For a, draw a picture, you will have 2 of each kind of side (6 sides, 4 the same in this case).

b)V= 9πh

c) 1/3(9)πh

http://www.coolmath.com

Answer 9

a. the SA=LA (Lateral area) + 2B (B:area of base)
LA=ph (p:perimeter of base h:height of figure)

b. the SA=LA+2B LA=2(pi)(r)(h) (r:radius h:height)

c. V=1/3(Bh) (B:area of base h: height )

Answer 10

i remember rec. prisims but not the rest:

2(aXb + aXc + bXc)= SA