Question

A balloon has a circumference of 28 in. Use the circumference to approximate the surface area of the balloon to the nearest square inch.

784 in2
2,463 in2
998 in2
250 in2

Answer 1

What is the slant height of the pyramid to the nearest tenth?

19.0 mm
12.5 mm
15.5 mm
13.9 mm

Answer 2

Using Euler’s Formula (F + V = E + 2), find the number of faces.

Vertices: 16
Edges: 37
Faces: ?

Answer 3

F=23 i think

Answer 4

for the Euler's formula one

Answer 5

ok thanks!

Answer 6

@jim_thompson5910

Answer 7

for the balloon problem

circumference = 2*pi*r where r is the radius of the balloon
we can solve for r by substituting 28 for the circumference

28 = 2*pi*r
r = 14/pi

surface area of a sphere = 4*pi*r^2
since r = 14/pi, we can plug in 14/pi into the surface area equation and solve for surface area

Answer 8

so do i do 2*3.14*14?

Answer 9

hm, not quite, we want to solve for r first

28 = 2*pi*r

we divide both sides by 2 pi, giving us

14/pi = r

then we use this value of r for the surface area equation

Answer 10

i got 87 23/25?

Answer 11

can you show me how you got that answer?

Answer 12

14/3.14 = 4 72/157

Answer 13

is that right?

Answer 14

well, yes, that would be the value of r

(let's convert to decimals in this case, it'll make it a bit easier for us later on)

r = 14/3.14 = 4.46

Answer 15

ok

Answer 16

then we can use this value of r for the surface area equation

surface area = 4*pi*r^2 = 4*3.14*(4.46)^2 = 249.8, which rounds to 250

Answer 17

oh okay thanks !

Answer 18

could u please help me with my second question above?

Answer 19

im not sure on this one either :/

What is the surface area of the pyramid to the nearest whole number?

30 cm2
25 cm2
60 cm2
85 cm2

Answer 20

let's focus on the slant height one first (the one you posted earlier)

the height of the pyramid is 12 and the its base is a square with side lengths of 7
if you look at the triangle inside the pyramid, you can see that it's a right triangle with legs 12 and 3.5 (since 7/2 = 3.5)

the slant height (the hypotenuse) can be found using the Pythagorean theorem

Answer 21

whats the pythagorean theorem?

Answer 22

oh a^2+b^2=c^2?

Answer 23

yeah

Answer 24

i got 156 1/4

Answer 25

remember to take the square root at the end

Answer 26

244414 1/16?

Answer 27

square root, not square

Answer 28

\[\sqrt{?} this on a an\]

Answer 29

yes

Answer 30

on a and b and c?

Answer 31

the pythagorean theorem tells us

(slant height)^2 = 12^2 + 3.5^2 = 156.25

to find slant height, we take the square root of both sides

Answer 32

220.9708691?

Answer 33

square root

slant height^2 = 156.25

slant height = square root of 156.25

Answer 34

12 1/2?

Answer 35

yup, you got it, do you understand what we did?

Answer 36

yes! thank you! and now can we do my next question ?

Answer 37

alright, it wants the surface area of the pyramid, which means we need to find the area of each of the 4 triangular faces + the area of the base

each of the triangles has base = 5 and height = 6

the area of a triangle can be found using the formula:
area = (1/2)(base)(height)

so the combined area of all the triangles is
4*(1/2)(base)(height)

next, we want to find the area of the base, which is a square with sides 5. the area of a square can be found using area = s^2

to find the final answer, add the area of the 4 triangles + area of the square

Answer 38

so putting everything together

base = 5
height = 6

surface area = 4*(1/2)(base)(height) + (base)^2

Answer 39

160?

Answer 40

but thats not on my answers

Answer 41

please check your calculations again

Answer 42

surface area = 4*(1/2)(6)(5) + (5)^2

Answer 43

85? so i was right then because i already have that answer checked?

Answer 44

yup, 85 is what I got too

Answer 45

What is the surface area of the right prism?

540 in2
486 in2
648 in2
972 in2

Answer 46

thanks!

Answer 47

surface area of a prism = 2*L*W + 2*W*H + 2*H*L
H = 18
W = 6
L = 9

Answer 48

*rectangular prism

Answer 49

648(:

Answer 50

What is the volume of the cone to the nearest tenth?

829.4 m3
1,520.5 m3
552.9 m3
1,244.1 m3

Answer 51

i think its a

Answer 52

(assuming that the radius is 11, kinda ambiguous from the diagram)

volume of cone = (1/3)(pi)*h*(r^2)
r = 11
h = 12

Answer 53

What is the surface area of the pyramid to the nearest whole number?

96 cm2
132 cm2
72 cm2
156 cm2

Answer 54

a is incorrect, please try my formula

Answer 55

i got 1519 19/25