Question

i need some questions checked

Answer 1

@Vocaloid

Answer 2

check your calculations again

volume of a cylinder = pi * r^2 * h

Answer 3

90.25 for the radius

Answer 4

1.27 for the height

Answer 5

the radius is just 9.5 not 90.25

Answer 6

643.3?

Answer 7

wait a sec

Answer 8

it's asking for the surface area not volume (since the penny is only coated w/ copper)

so the formula ends up being SA = 2*pi*r*h + 2*pi*r^2 plug in r and h

Answer 9

uh, can you plug those in real quick?

Answer 10

i gotta run a quick errand

Answer 11

r is 9.5 as stated before
h is 1.27

SA = 2*pi*r*h + 2*pi*r^2
=

2*pi*1.27*9.5 + 2*pi*9.5^2

Answer 12

642.8

Answer 13

be careful with order of operations

start by calculating

2*pi*9.5^2 and 2*pi*1.27*9.5 separately then add them together

Answer 14

plug 2*pi*9.5^2 into a calculator and write the result down

plug 2*pi*1.27*9.5 into a calculator and write the result down

then add them together

Answer 15

567 and 75.8

Answer 16

ugh apparently I had the wrong thing typed in

anyway 2*pi*9.5^2 + 2*pi*1.27*9.5 becomes 642.86 which rounds up to 642.9 = your sol'n

Answer 17

SA = 2*pi*r*h + 2*pi*r^2 again

plug in r and h

Answer 18

477.5

Answer 19

good

Answer 20

true?

Answer 21

this one is actually false, lateral area excludes the top/bottom bases

Answer 22

so use the same equation for this, right?

Answer 23

it's asking for lateral area not surface area

so simply find the perimeter of the octagon and then multiply by the height

Answer 24

an octagon has eight equal sides

so its perimeter is 8 * side length.

Answer 25

65.7

Answer 26

6.5 is the height and 7.4 is the side length

Answer 27

if 7.4 is the side length what is the perimeter?

Answer 28

6.5

Answer 29

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Mercury
an octagon has eight equal sides

so its perimeter is 8 * side length.
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 30

the side length as we established is 7.4

therefore perimeter = 8*7.4

all that's left is to multiply by the height 6.5.

Answer 31

384.8

Answer 32

good so that's your solution

Answer 33

D?

Answer 34

good

Answer 35

true?

Answer 36

good

Answer 37

check your calculations again

let's start with the two triangle sides. height 3, base 4, what's the combined area of both triangles?

Answer 38

remember the formula for the area of a triangle is (1/2)bh.

Answer 39

6

Answer 40

good but we want to know the area of both triangles so double that to get 12

now let's look at the three remaining faces

you have a rectangle with side lengths 5 and 13
a rectangle with side lengths 4 and 13
and a rectangle with side lengths 3 and 13

calculate the sum of these areas

Answer 41

i got it now

Answer 42

still working

i keep getting something that's not one of the choices

Answer 43

alright finally figured out where i was going wrong

you need to calculate the height of the triangle on the dotted line

so its a right triangle with hypotenuse 10 and leg 12/2 calculate the other leg

Answer 44

i'm getting confused now...

Answer 45

check the circled triangle

notice how you have a right triangle with leg 6 and hypotenuse 10

calculate the length of the other leg.

Answer 46

like, 4?

Answer 47

use the Pythagorean theorem

Answer 48

136

Answer 49

leg^2 + leg^2 = hypotenuse^2
plug in the hypotenuse, leg, and solve for the other leg

Answer 50

leg = 6
hypotenuse = 10

6^2 + leg^2 = 10^2

solve for leg.

Answer 51

8

Answer 52

good

so 8 gives us the height of the triangle

we already know the base is 12

so area = (1/2)bh = (1/2)8*12

we have two triangles so just double that to get

8*12 = 96, then we keep going w/ the other sides

Answer 53

we have one big side on the front that's 12 * 12

and two smaller rectangular sides that are 10 * 12 each

so 12 * 12 + 2(10*12) + 96 from before = 480 = your solution

Answer 54

hm not quite let's check your calculations again

let's start w/ the walls of the building

two walls that are 8*6 and two walls that are 6*6

gives us 2(8*6) + 2(6*6)

Answer 55

then, we add the top which is another 8*6 side

we subtract the area where the smokestack and ceiling touch

so - (0.5)^2 * pi from that

finally we add the painted area of the smokestack which is just 2*pi*r*h = 2*pi*0.5*3

Answer 56

putting it all together

2(8*6) + 2(6*6) + 8*6- (0.5)^2 * pi + 2*pi*0.5*3 = ?

Answer 57

for the sake of time after you plug this into a calculator it's 224.6 = your solution.

Answer 58

sorry, i'm not really working at full capacity today...

Answer 59

@Mercury

Answer 60

close but not quite

the amt. of material to make a box is equal to its surface area

a cube has 6 sides

so 6 * area of each side

Answer 61

so it was just 60?

Answer 62

6*10*10 = 600 not 60

Answer 63

sorry

Answer 64

let me ask someone b/c i'm not quite sure i understand what they're looking for

Answer 65

ok

Answer 66

alright i got it

Answer 67

let's start w/ the semicircle

circumference is 2pi*r as usual

we only have half the circle so (1/2) * 2pi*r or just pi*r, or 2pi

multiplying this by the thickness of the arch (1ft) just gives us 2pi * 1 for the semicircular part

Answer 68

wait, is r 4 or 7?

Answer 69

notice how the top part of the arch has diameter 4 as shown in the original picture

so the radius is 1/2 the diameter, or 2

Answer 70

moving on to the rectangular parts, we saw that the top part of the arch is 2 ft and the total height of the arch is 7 feet

so the part of the arch without the circular dome part is 5 feet tall

the two wooden parts on the left and right side of the arch are 1 foot wide

so area of each rectangular piece on the side is 1 * 5 = 5

since there are two of them, we double to get 10

Answer 71

adding everything together:

10 from the rectangular pieces + 2pi from the arch part gives us about ~16.3 feet when you chuck this into a calculator so 16.3 is the best choice out of all of them

Answer 72

if you're having some trouble understanding try to visualize the arch first as a 2dimensional figure like this

Answer 73

since 4 is essentially the diameter of the semicircle, divide 4/2 to get the radius 2

Answer 74

(sorry for the crappy diagram but) since we have a semicircle, we can draw any line segment from the center to the edge to get another segment with length 2

Answer 75

now, we know the circular part + rectangular part combined have a height of 7 feet

subtracting the 2 feet from the "dome" circular part, we get 5 as the height of the rectangular part

Answer 76

then we switch back to a 3-d view of the image

Answer 77

sorry if this is kind of overwhelming

Answer 78

it's perfectly fine.

Answer 79

@Mercury so the equation is to just multiply pi with the diameter or something?

Answer 80

hm

perhaps I could explain it another way

imagine if we took the arch and "unrolled" it into a giant rectangle

Answer 81

where the entire length of the arch becomes the length of this rectangle

and the width of the arch becomes the width of this new rectangle

Answer 82

we already know how wide the arch is (1 foot), but we need to do a bit of work to find the length

we can see that the arch has a rectangular part underneath the semicircle. so we just need to find the circumference of the semicircle + the lengths of the sides to find the length of the long rectangle when the arch is "unrolled"

Answer 83

using these calculations, we can see that the arch (from a 2d perspective) is composed of:

1) a rectangle with length 5
and
2) a semicircle with radius 2

Answer 84

we have two rectangular sides (5 each, so 5+5 = 10)
and a semicircle

which we can find the circumference by taking (1/2)*2*pi*r or just pi*r

the entire diameter of the circular part is 4 (see the original diagram) so the radius is just 2

therefore the circumference is pi*r = 2*pi

Answer 85

so adding up all these lengths together:

5 + 5 + 2*pi === > the length of the entire arch when "unrolled"

1 is the width

and as usual, area of a rectangle is L*W

so (5+5+2pi)*1 ==> area of the entire arch when unrolled, and thus the solution

Answer 86

alright

Answer 87

16.3

Answer 88

good

Answer 89

good

Answer 90

hm not quite

we want the lateral surface area so pi*r^2 * h
plug in r and h and pi

Answer 91

D

Answer 92

good

Answer 93

hm not quite

pi*r^2 * h

check your calculations again

Answer 94

pi*2^2*11

Answer 95

B

Answer 96

the 4 lateral faces are the triangles which ~do~ meet at the vertex (apex) so the original statement is true

Answer 97

if we try shading in this right triangle over here:

Answer 98

we can see we have a right triangle with legs 15 and 20 (since the bottom leg is half the length of one side)

use the pythagorean theorem to find the hypotenuse first

Answer 99

625

Answer 100

almost, remember the pythagorean theorem gives you the square of a side

so we take the sqrt of 625 to get 25 as the hypotenuse

with that being said we go back to the original pyramid:

Answer 101

now we can see each side of the triangle has height 25 and base 40

calculate the area of one triangle (using area = 1/2 * b * h) and multiply by 4 to get the lateral area

Answer 102

so 25?

Answer 103

no, 15

Answer 104

(1/2)bh * 4

=

(1/2)(25)(40) * 4

Answer 105

75

Answer 106

right?

Answer 107

@Mercury

Answer 108

@sammixboo

Answer 109

Yo my wifi randomly cut out last night sorry about that :/

Answer 110

@vocaloid @Mercury that's alright, should we continue now though?