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Math Help - Help me Please!

  1. #1
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    Help me Please!

    I've got some questions that I just don't get! Hopefully you guys can help me solve them.

    1. The edge of a cube is 4 cm. What is its volume? _________ It's lateral surface? ______ It's total surface? _________

    2.Mr. Ryan is digging a cylindrical cistern. It is to be 5 m deep and 2 m in diameter. How much dirt must be removed in digging it?

    3. What change would be made in the volume of a cylinder by doubling the radius of the base and keeping the height the same?

    What change would be made in the curved surface?

    4. A boat sails 3 km due east and then 3 1/2 (one-half) due south. How far is the boat now from its starting point? (Correct the answer to 2 significant figures)

    5. The length of a diagonal of a square is 18. Find its area.

    6. Find the area of a square inscribed in a circle of a radius of 5cm.

    Thanks you guys!!
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Rocher View Post
    I've got some questions that I just don't get! Hopefully you guys can help me solve them.

    1. The edge of a cube is 4 cm. What is its volume? _________ It's lateral surface? ______ It's total surface? _________

    2.Mr. Ryan is digging a cylindrical cistern. It is to be 5 m deep and 2 m in diameter. How much dirt must be removed in digging it?

    3. What change would be made in the volume of a cylinder by doubling the radius of the base and keeping the height the same?

    What change would be made in the curved surface?

    4. A boat sails 3 km due east and then 3 1/2 (one-half) due south. How far is the boat now from its starting point? (Correct the answer to 2 significant figures)

    5. The length of a diagonal of a square is 18. Find its area.

    6. Find the area of a square inscribed in a circle of a radius of 5cm.

    Thanks you guys!!
    for the first question, do you mean the lateral surface area and total surface area?
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    Yeah, that was what the question said, but I'm positive it states about area.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Rocher View Post
    I've got some questions that I just don't get! Hopefully you guys can help me solve them.

    1. The edge of a cube is 4 cm. What is its volume? _________ It's lateral surface? ______ It's total surface? _________
    Volume of a cube is length times width times height, and the length, width and height are equal for a cube, so the volume is:

    V = 4*4*4 = 64 cm^3

    it's lateral surface area is the surface area of all the sides excluding the base (if the roof of an object is parallel to it's base, it is also considered a base). so the lateral surface area of a cube, will be the area of 4 faces, which is:

    A = area of face 1 + area of face 2 + area of face 3 + area of face 4
    ...= 4*4 + 4*4 + 4*4 + 4*4
    ...= 64 cm^2

    the total surface area of a cube is the area of all the faces, that is a total of 6 faces. so the total surface area is given by:

    S = 4*4 + 4*4 + 4*4 + 4*4 + 4*4 + 4*4
    ...= 96 cm^2

    2.Mr. Ryan is digging a cylindrical cistern. It is to be 5 m deep and 2 m in diameter. How much dirt must be removed in digging it?
    this is talking about the volume of dirt that has to be removed, which will be equal to the volume of the cylinder. the volume of a cylinder is given by:

    V = pi*r^2 * h
    where r is the radius and h is the height

    so, V = pi*(1 m)^2 * (5 m) = 5pi m^3 ~=15.708 m^3

    3. What change would be made in the volume of a cylinder by doubling the radius of the base and keeping the height the same?

    What change would be made in the curved surface?
    Recall, the volume V of a cylinder is given by:
    V = pi*r^2 * h
    if we double the radius, then
    V = pi*(2r)^2 * h = 4pi*r^2 * h

    so by doubling the radius, we quadruple the volume (that is, increase the volume 4 times, or by a factor of 4)

    The curved surface are of a cylinder is given by:
    C = 2pi*r*h
    if we double the radius, then:
    C = 2pi*(2r)*h = 2*2pi*r*h

    so by doubling the radius, we double the curved surface area

    4. A boat sails 3 km due east and then 3 1/2 (one-half) due south. How far is the boat now from its starting point? (Correct the answer to 2 significant figures)
    i'll get back to this one, i'd like to draw a diagram for it

    5. The length of a diagonal of a square is 18. Find its area.
    i'd also like to draw a diagram for this, but o well, let's use our imaginations.

    if we draw one diagonal of a square, we create two right angled triangles, each with a hypotenuse the length of the diagonal. draw it to see what i'm talking about. now, the other two sides of each triangle will be equal, since it's a square. let's find the length of the other two sides, or one of the other two sides as it were.

    By pythagoras,

    18^2 = a^2 + b^2
    where a and b are the lengths of the other two sides. since they are equal, we can represent them with one variable, say a, so
    18^2 = a^2 + a^2 = 2a^2
    => a = sqrt[(18^2)/2] = sqrt(162) ~= 12.728

    now the area of a triangle is given by:
    A = (1/2)base*height
    so here,
    A = (1/2)sqrt(162)*sqrt(162) = (1/2)*162 = 81 squared units.

    so the area of the square is 2*area of one triangle = 2*81 = 162 squared units

    6. Find the area of a square inscribed in a circle of a radius of 5cm.
    we need a diagram for this as well, so we'll come back to it


    if you have any questions on what i've done so far, ask
    Last edited by Jhevon; May 4th 2007 at 09:47 PM.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Rocher View Post

    4. A boat sails 3 km due east and then 3 1/2 (one-half) due south. How far is the boat now from its starting point? (Correct the answer to 2 significant figures)
    See the diagram below

    Let A be the starting point, so we start at A and sail 3 km east to point B, then 3.5 km south to point C. we want to find our distance from the starting point, that is, the distance between A and C. Obviously we form a right-angled triangle here. we have the length of two sides and we want to find the length of the hypotenuse. thus we will employ Pythagoras' theorem.

    (AC)^2 = (AB)^2 + (BC)^2
    ...........= (3)^2 + (3.5)^2
    ...........= 21.25 = 85/4
    => AC = sqrt(85/4) = sqrt(85)/2 km
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Rocher View Post
    6. Find the area of a square inscribed in a circle of a radius of 5cm.
    See the diagram below

    we see that if we connect the center O to one of the vertices of the square, we have the length of the radius connecting it. if we extend that line to connect the opposite vertex, we have the diagonal of the circle, which is 2*radius = 2*5 = 10.

    now you see we have a right angled triangle, so we can find the area of the square by finding the area of the two triangles. their area will be the same, so let's find the area of one and multiply it by 2.

    first let's find the length of sides AB and BC, and note AB = BC, so let's call their lengths a. we have by Pythagoras theorem:

    10^2 = a^2 + a^2 = 2a^2
    => a = sqrt[(10^2)/2] = sqrt(50) = sqrt(25*2) = sqrt(25)*sqrt(2) = 5sqrt(2)

    so the area of triangle ABC is given by:
    A = (1/2)base*height = (1/2)[5sqrt(2)]*[5sqrt(2)] = 25 cm^2

    so the area of the square is
    A = 2*25 = 50 cm^2
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  7. #7
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    Thank you very very much!!
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