## mckenzieandjesus one year ago 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

1. mckenzieandjesus

What is the slant height of the pyramid to the nearest tenth? 19.0 mm 12.5 mm 15.5 mm 13.9 mm

2. mckenzieandjesus

Using Euler’s Formula (F + V = E + 2), find the number of faces. Vertices: 16 Edges: 37 Faces: ?

3. anonymous

F=23 i think

4. anonymous

for the Euler's formula one

5. mckenzieandjesus

ok thanks!

6. mckenzieandjesus

@jim_thompson5910

7. Vocaloid

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

8. mckenzieandjesus

so do i do 2*3.14*14?

9. Vocaloid

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

10. mckenzieandjesus

i got 87 23/25?

11. Vocaloid

|dw:1435442689088:dw|

12. Vocaloid

can you show me how you got that answer?

13. mckenzieandjesus

14/3.14 = 4 72/157

14. mckenzieandjesus

is that right?

15. Vocaloid

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

16. mckenzieandjesus

ok

17. Vocaloid

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

18. mckenzieandjesus

oh okay thanks !

19. mckenzieandjesus

20. mckenzieandjesus

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

21. Vocaloid

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

22. Vocaloid

|dw:1435443114081:dw|

23. mckenzieandjesus

whats the pythagorean theorem?

24. Vocaloid

|dw:1435443244024:dw|

25. mckenzieandjesus

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

26. Vocaloid

yeah

27. mckenzieandjesus

i got 156 1/4

28. Vocaloid

remember to take the square root at the end

29. mckenzieandjesus

244414 1/16?

30. Vocaloid

square root, not square

31. Vocaloid

|dw:1435443406104:dw|

32. mckenzieandjesus

$\sqrt{?} this on a an$

33. Vocaloid

yes

34. mckenzieandjesus

on a and b and c?

35. Vocaloid

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

36. mckenzieandjesus

220.9708691?

37. Vocaloid

square root slant height^2 = 156.25 slant height = square root of 156.25

38. mckenzieandjesus

12 1/2?

39. Vocaloid

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

40. mckenzieandjesus

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

41. Vocaloid

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

42. Vocaloid

so putting everything together base = 5 height = 6 surface area = 4*(1/2)(base)(height) + (base)^2

43. mckenzieandjesus

160?

44. mckenzieandjesus

but thats not on my answers

45. Vocaloid

46. Vocaloid

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

47. mckenzieandjesus

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

48. Vocaloid

yup, 85 is what I got too

49. mckenzieandjesus

What is the surface area of the right prism? 540 in2 486 in2 648 in2 972 in2

50. mckenzieandjesus

thanks!

51. Vocaloid

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

52. Vocaloid

*rectangular prism

53. mckenzieandjesus

648(:

54. mckenzieandjesus

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

55. mckenzieandjesus

i think its a

56. Vocaloid

(assuming that the radius is 11, kinda ambiguous from the diagram) volume of cone = (1/3)(pi)*h*(r^2) r = 11 h = 12

57. mckenzieandjesus

What is the surface area of the pyramid to the nearest whole number? 96 cm2 132 cm2 72 cm2 156 cm2

58. Vocaloid

a is incorrect, please try my formula

59. mckenzieandjesus

i got 1519 19/25

60. Vocaloid

which is closest to answer b (probably because of rounding)

61. mckenzieandjesus

19/25 as a decimal is 0.760

62. mckenzieandjesus

thanku

63. Vocaloid

and for the last one, it's asking for the surface area of the pyramid. the last problem you posted is very similar to the third problem you posted (surface area of a pyramid), just with different numbers. perhaps you look at my work and solve it on your own? :)

64. Vocaloid

helpful reminder: surface area of pyramid = area of 4 triangles + area of square base

65. mckenzieandjesus

so (1/3)*3.14*8*(6^2) = 301 11/25

66. Vocaloid

wrong formula. area of triangle = (1/2)(base)(height) area of square = (base)^2

67. mckenzieandjesus

so 24 and 36

68. Vocaloid

right, and there are 4 triangles and 1 square so surface area = 4*area of triangle + area of squrae

69. mckenzieandjesus

132

70. Vocaloid

great

71. mckenzieandjesus

do you know anything about this figure? What is the volume of the composite figure? 192 ft3 76 ft3 152 ft3 96 ft3

72. Vocaloid

hint: it's 2 prisms put together|dw:1435446620974:dw|

73. Vocaloid

find the volume of prism A and add to the volume of prism B volume = L*W*H volume of A = (4)(2)(8) volume of B = (2)(2)3)

74. mckenzieandjesus

do u know what part would be length?

75. mckenzieandjesus

oh nvrm

76. Vocaloid

|dw:1435446845195:dw|

77. mckenzieandjesus

A= 64 B= 12

78. Vocaloid

right, so keep going

79. mckenzieandjesus

what do i do next?

80. mckenzieandjesus

64+12= 76

81. Vocaloid

right

82. mckenzieandjesus

ok thanku

83. mckenzieandjesus

What is the volume of the square pyramid? Round to the nearest tenth. 40.0 cm3 480.0 cm3 147.3 cm3 720.0 cm3

84. Vocaloid

volume of square pyramid = (1/3)(L)(W)(H)

85. mckenzieandjesus

480?

86. Vocaloid

great

87. mckenzieandjesus

wouldnt this be rectangle? Describe the cross section of the rectangular prism. rectangle hexagon trapezoid triangle

88. Vocaloid

yup, good job

89. mckenzieandjesus

thank you for all your time and effort to help me!(:

90. Vocaloid

no problem, I'm glad I was able to help