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anonymous

  • 5 years ago

A hemisphere has a volume of 18π cm3. Find its radius

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  1. dumbcow
    • 5 years ago
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    Volume is half that of a sphere V=(1/2)*(4/3)*pi*r^3 = 18pi -> 2/3 r^3 = 18 ->r^3 = 18*(3/2) -> r^3 = 27 = 3*3*3 r=3

  2. anonymous
    • 5 years ago
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    A sphere has a volume of 972π in.3. Find its radius.

  3. dumbcow
    • 5 years ago
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    same as above V = 4/3 pi r^3 = 972 solve for r

  4. anonymous
    • 5 years ago
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    A triangular pyramid has a volume of 180 cm3 and a height of 12 cm. Find the length of a side of the triangular base if the triangle’s height from that side is 6 cm.

  5. dumbcow
    • 5 years ago
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    volume of pyramid is area of base(B)*height V = B*12 = 180 B = 180/12 = 15 Area of base is area of triangle A = 1/2 * length(L)*height = 15 1/2*6*L = 15 solve for L

  6. dumbcow
    • 5 years ago
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    oops i messed up volume of pyramid is 1/3* B*h correction 1/3*B*12 = 180 B = 180/4 = 45 ... A=1/2*6*L = 45

  7. anonymous
    • 5 years ago
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    l is 45

  8. dumbcow
    • 5 years ago
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    no (1/2)*6*L = 45 solve for L by multiplying 6 and 1/2, then dividing on both sides

  9. anonymous
    • 5 years ago
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    i got 15

  10. dumbcow
    • 5 years ago
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    correct, good job

  11. anonymous
    • 5 years ago
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    The volume of a cylinder is 628 cm3. Find the radius of the base if the cylinder has a height of 8 cm. Round your answer to the nearest 0.1 cm.

  12. dumbcow
    • 5 years ago
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    ok for this one can you tell me the volume formula for cylinder?

  13. anonymous
    • 5 years ago
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    basexheight

  14. dumbcow
    • 5 years ago
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    good base is a circle, whats the area of a circle?

  15. anonymous
    • 5 years ago
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    pir^2

  16. dumbcow
    • 5 years ago
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    good V = (pir^2)*h pi*r^2*8 = 628

  17. dumbcow
    • 5 years ago
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    multiply 8*pi divide on both sides

  18. anonymous
    • 5 years ago
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    78.5

  19. dumbcow
    • 5 years ago
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    dont forget about pi (use3.14) r^2 = 78.5/pi divide 78.5/3.14 then take the square root to get r

  20. anonymous
    • 5 years ago
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    4.99

  21. dumbcow
    • 5 years ago
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    correct

  22. dumbcow
    • 5 years ago
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    actually with rounding to nearest .1 it would just be 5

  23. anonymous
    • 5 years ago
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    Sylvia has just discovered that the valve on her cement truck failed during the night and that all the contents ran out to form a giant cone of hardened cement. To make an insurance claim, she needs to figure out how much cement is in the cone. The circumference of its base is 44 feet, and it is 5 feet high. Calculate the volume to the nearest cubic foot.

  24. dumbcow
    • 5 years ago
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    to answer this we need to find radius what is circumference of circle

  25. anonymous
    • 5 years ago
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    so that mean 22

  26. dumbcow
    • 5 years ago
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    good but we still need to divide by pi (3.14)

  27. dumbcow
    • 5 years ago
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    2pi*r =44 pi*r=22 r=22/pi

  28. anonymous
    • 5 years ago
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    7.00

  29. dumbcow
    • 5 years ago
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    good next we use volume of cone formula

  30. anonymous
    • 5 years ago
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    so that i use 1/3bh

  31. anonymous
    • 5 years ago
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    really all you need to do to solve these problems is just write out the sets of equations that apply to the problem for example the circumference equation and the volume of a cone. then, you plug in what you know such as the measurement of circumference to solve for the radius then plug that into the volume of a cone formula.

  32. dumbcow
    • 5 years ago
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    yes b = area of circle w/ radius of 7

  33. anonymous
    • 5 years ago
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    use what you do know to find what you don't

  34. anonymous
    • 5 years ago
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    49pi

  35. dumbcow
    • 5 years ago
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    good V = 1/3 * 49pi*5 multiply it out

  36. anonymous
    • 5 years ago
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    with pi?

  37. dumbcow
    • 5 years ago
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    yes

  38. anonymous
    • 5 years ago
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    256.56

  39. dumbcow
    • 5 years ago
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    good now round to nearest foot

  40. anonymous
    • 5 years ago
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    257

  41. anonymous
    • 5 years ago
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    don't forget your units

  42. dumbcow
    • 5 years ago
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    yep ok i gotta go keep doing these steps, find correct formula plug in numbers you you solve for ones you don't good luck

  43. dumbcow
    • 5 years ago
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    thanks kristo, forgot about that

  44. anonymous
    • 5 years ago
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    no problem

  45. anonymous
    • 5 years ago
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    A sealed rectangular container 6 cm by 12 cm by 15 cm is sitting on its smallest face. It is filled with water up to 5 cm from the top. How many centimeters from the bottom will the water level reach if the container is placed on its largest face?

  46. anonymous
    • 5 years ago
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    alright first you need to find the volume of the water on its smallest face

  47. anonymous
    • 5 years ago
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    1080

  48. anonymous
    • 5 years ago
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    one sec i will be right back...

  49. anonymous
    • 5 years ago
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    ok i'm back

  50. anonymous
    • 5 years ago
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    so what might be a good idea is to draw a picture first which face would be the smallest?

  51. anonymous
    • 5 years ago
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    i drew what next

  52. anonymous
    • 5 years ago
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    okay so what you have is a rectangular prism with a base of 6x12 (the smallest face) making the height without water 15

  53. anonymous
    • 5 years ago
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    so the height of the water is five cm from the top so you subtract five from fifteen to get the height of the water

  54. anonymous
    • 5 years ago
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    that make 72

  55. anonymous
    • 5 years ago
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    720 6x12x10 remember to include WxLxH

  56. anonymous
    • 5 years ago
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    then

  57. anonymous
    • 5 years ago
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    now we have the volume what we don't know is what the height of the water is when the container is set on its largest face

  58. anonymous
    • 5 years ago
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    so i would draw a picture of the new rectangle first what is the W and the L of the base?

  59. anonymous
    • 5 years ago
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    hint: largest face

  60. anonymous
    • 5 years ago
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    12 and 10

  61. anonymous
    • 5 years ago
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    12 and 15

  62. anonymous
    • 5 years ago
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    180

  63. anonymous
    • 5 years ago
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    we only subtracted five to find the height of the water when the container was on the small face, since we have the W and L now we solve for the height using the volume formula V=WxLxH

  64. anonymous
    • 5 years ago
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    use the volume formula we found before 720

  65. anonymous
    • 5 years ago
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    720=15x12xH

  66. anonymous
    • 5 years ago
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    i got 4 for height

  67. anonymous
    • 5 years ago
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    great

  68. anonymous
    • 5 years ago
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    now subtract that from six since it wants the height from the top of the prism

  69. anonymous
    • 5 years ago
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    2

  70. anonymous
    • 5 years ago
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    yes

  71. anonymous
    • 5 years ago
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    do you really understand how we got that?

  72. anonymous
    • 5 years ago
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    well some of the time

  73. anonymous
    • 5 years ago
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    try to image a cereal box, you have the box standing up. you know how high the cereal is from the top of the box you use that to find the volume of the cereal. then you tip the box on its larger face then you want to know what the height of the cereal is from the new top edge of the box

  74. anonymous
    • 5 years ago
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    does that help to picture the problem a little better?

  75. anonymous
    • 5 years ago
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    yes so BxH

  76. anonymous
    • 5 years ago
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    yes!

  77. anonymous
    • 5 years ago
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    or length times width times height = volume

  78. anonymous
    • 5 years ago
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    but you got the concept

  79. anonymous
    • 5 years ago
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    i have to sleep now but good luck

  80. anonymous
    • 5 years ago
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    we know that 4 is the height so we need to find the base

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