The slant height, l, of a cone with a surface area of 500π ft2 and a radius of 15 ft.

The slant height, l, of a cone with a surface area of 500π ft2 and a radius of 15 ft.

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  1. Cone Surface Area = PI * radius * slant height

    slant height = surface area / (PI * radius)

    slant height = 500 / (PI * 15)

    slant height = 10.6103295395 feet

    Step-by-step explanation:

  2. Slant height = 18 .33 feet.

    Step-by-step explanation:

    Given : A cone with a surface area of 500π ft² and a radius of 15 ft.

    To find : find the slant height l .

    Solution : We have given

    Surface area of cone = 500π  ft².

    Radius = 15 ft.

    Surface area of cone  = π * radius ( radius + slant height ) .

    Plug all the values.

    500 π = π * 15 ( 15 + slant height ) .

    On dividing both sides by π

    500 = 15 ( 15 + slant height ) .

    On dividing both sides by 15

    33.33 = 15 + slant height .

    On subtracting both sides by 15.

    33.33 -15 = slant height .

    Slant height = 18 .33 feet.

    Therefore , Slant height = 18 .33 feet.

  3. we know that

    The formula of the surface area of the cone is equal to

    [tex]SA=\pi r^{2}+\pi rl[/tex]

    where

    SA is the surface area

    r is the radius of the cone

    l is the slant height

    in this problem we have

    [tex]SA=500\pi\ ft^{2}\\r=15\ ft\\l=?[/tex]

    Solve the formula for l

    [tex]SA=\pi r^{2}+\pi rl\\ \\\pi rl=SA-\pi r^{2} \\ \\l=\frac{SA-\pi r^{2} }{\pi r}[/tex]

    substitute the values

    [tex]l=\frac{500\pi -\pi 15^{2} }{\pi15}\\ \\l=\frac{275}{15}\ ft\\ \\l=\frac{55}{3}\ ft\\ \\l=18\frac{1}{3}\ ft[/tex]

    therefore

    the answer is

    The slant height is [tex]18\frac{1}{3}\ ft[/tex]

  4. The formula for the slant height of a cone is , where S is surface area of the cone. Use the formula to find the slant height, l, of a cone with a surface area of 500π ft2 and a radius of 15 ft. l = ft         275 ft

  5. Given:
    formula for the slant height of a cone is I= s-π(pie)r^2 over π(pie)
    where S is surface area of the cone
    S(surface area) = 500π ft^2
    r(radius) = 15 ft

    Required:
    l in m

    Solution:
    I = (s - πr²) / π
    I = (500π - π(15)²) / π
    l = 275 ft (1m / 3.2808 ft)
    l = 83.82 m

  6. The slant height of the cone with the given measurements would be would be around 18.3164 ft.

    You can use cone formulas to get to this answer to find the slant height.

    I hope this helps 🙂

  7. 275 ft

    Step-by-step explanation:

    The formula given to use for the slant height l of the cone is ;

    l = (s - πr^2)/π

    Now substituting the parameters given in the question, 500 π for area and radius of 15, we have

    l = {500π-15^(2)π}/π

    l =( 500 π -225 π)/π

    l = 275 π/π

    l = 275 ft

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