How to add pi and math questions?

Im confused about something... my teacher was doing a formula for surface area he had something like 36 pi + 64 pi and together its 100 pi... should it not be pi squared or something?

I tried something similar right now, i had two sets of 2 pi that i divided by a number, and got one answer, when i combined them to make 4 pi i got a different answer...

BONUS IF ANYONE CAN EXPLAIN THESE PROBLEMS OR ANY ONE OF THEM:

A cone has a surface area of 100mm squared The height is twice the radius. What is the height of the cone?

A rectangular prism which a length and width of 10cm and a height of 20cm is half full of juice. A round ball with a diameter of 4cm is dropped into this rectangular prism. How far will the water level rise once the sphere is completely underwater?

A ball has a diameter of 10cm estimate the height of the smallest box in which the ball will fit in in inches

4 Answers

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  • 5 years ago
    Favorite Answer

    36 pi + 64 pi = ( 36 + 64) * pi

    = (100) *pi

    = 100pi

    Let r = radius, then h = 2r

    Surface area of a cone is given by

    S = pi*r *l + pi * r^2, ...........(1) where l is the slant height

    Now l^2 = r^2 + (2r)^2

    = r^2 + 4r^2

    = 5r^2

    l = r * sqrt(5)

    Now put this in equation (1)

    S = pi * r * r sqrt(5) + pi*r^2

    = pi*r^2sqrt(5) + pi*r^2

    = r^2 ( pisqrt(5) + pi)

    Therefore

    r^2 ( pisqrt(5) + pi) = 100

    r^2 = 100/[pisqrt(5) + pi]

    r = sqrt[ 100/[pisqrt(5) + pi] ]

    h = 2 sqrt[ 100/[pisqrt(5) + pi] ]

    = 2 sqrt(9.836)

    = 2* 3.136290234

    = 6.272580468

    = 6 . 3 mm

    Let h = rise

    Then

    100h = 4/3 pi r^3

    = 4/3 pi (2)^3

    = 32/3 pi

    = 33.51032164

    h = 0. 335 cm

  • 5 years ago

    36π + 64π = 100π

    (1)

    A cone has a surface area of 100mm squared The height is twice the radius. What is the height of the cone?

    SOLUTION

    Area of a cone = πr[r+√(h²+r²)]

    Let the surface area of the cone be,100mm² (Given):

    Let the height of the cone be, h

    Let the radius of the cone be, r

    The height is twice the radius means

    h = 2r

    Now from the formula:

    Area of a cone = πr[r+√(h²+r²)]

    Area = 100mm², r = r mm, h = 2r mm

    100 = πr[r+√{(2r)²+r²}]

    100 = πr[r+√(4r²+r²)]

    100 = πr[r+√(5r²)]

    Divide both side by πr

    100/πr = r + √(5r²)

    Take r to the other side. .

    (100/πr) - r = √(5r²)

    Square both side to get. ..

    [√(5r²)]² = [(100/πr) - r]²

    5r² = (100/πr - r)(100/πr - r)

    Expand the Right hand side to get. .

    5r² = (10000/π²r²)-(100r/πr)-(100r/πr)+r²

    5r² = (10000/π²r²)-(100/π)-(100/π)+r²

    5r² = (10000/π²r²)-2(100/π)+r²

    But π = 22/7 (constant). .

    π² = (22/7)² = 484/49

    5r²=[10000/(484/49)r²]-2[100/(484/49)]+r²

    5r²=[490,000/484r²]-2[4,900/484]+r²

    5r² = (122500/121r²)-2(1225/121)+r²

    Take r² to the other side

    5r²-r² = (122500/121r²)-(2450/121)

    4r² = (122500/121r²)-(2450/121)

    Find the L.C.M on the Right hand side..

    4r² = (122500 - 2450r²)/121r²

    Cross multiply to get ...

    484r⁴ = 122500 - 2450r²

    Re arrange to form an equation..

    484r⁴ + 2450r² - 122500 = 0

    This can be re write as .....

    484(r²)² + 2450r² - 122500 = 0

    Divide through by 2 to reduce the equation

    242(r²)² + 1225r² - 61250 = 0

    Using quadratic formula...

    a = 242, b = 1225, c = -61250

    r² = [-b ± √(b² - 4ac)]/2a

    r² = [-1225±√(1225)²-4(242)(-61250)]/(2×242)

    r² = [-1225±√(1500625+59290000)]/(484)

    r² = [-1225±√(60790625)]/(484)

    r² = (-1225 ± 7796.834293)/(484)

    r² = (-1225/484)±(7796.834293/484)

    r² = -2.5310 ± 16.1092

    r² = (-2.5310+16.1092) or (-2.5310-16.1092)

    r² = 13.5782 or r² = -18.6402

    Since negative is not allowed..

    r² = 13.5782

    Take the square root of both side

    √(r²) = √(13.5782)

    ∴ r = 3.68486092

    ∴ r = 3.68

    Since, h = 2r

    ∴ h = 2(3.68)

    ∴ h = 7.36 mm

    Therefore, the height of the cone, h = 7.36 mm

    One after the other.

  • Robert
    Lv 7
    5 years ago

    Instead of π, think of pies.

    Then what's 36 pies plus 64 pies?

  • DWRead
    Lv 7
    5 years ago

    You've forgotten the distributive rule!

    36π + 64π = (36+64)π = 100π

    :::::

    r, h, and ℓ are the radius, height, and slant length, respectively.

    lateral area = πrℓ

    base area = πr²

    surface area = πrℓ + πr²

    "A cone has a surface area of 100mm squared"

    πrℓ + πr² = 100

    "The height is twice the radius"

    h = 2r

    h² + r² = ℓ²

    4r² + r² = ℓ²

    ℓ = r√5

    πr(r√5) + πr² = 100

    πr²√5 + πr² = 100

    πr²(1+√5) = 100

    r² = 100/(π(1+√5))

    r = 10/√(π(1+√5))

    h = 20/√(π(1+√5))

    you can do the calculation

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