find its slant height for volume of a right circular cone is 100¦Ð cm3 and its height is 12cm.
volume of cone = (1/3)π r^2 h
I have a feeling that your 100¦Ð is supposed to mean 100π
so (1/3)π r^2 (12) = 100π
12r^2 = 300
r^2 = 300/12 = 25
r = 5
let the slant height be s
s^2 = 5^2 + 12^2
etc
To find the slant height of a right circular cone, we can first use the formula for the volume of a cone and then solve for the slant height.
The formula for the volume of a right circular cone is given by:
V = (1/3) * π * r^2 * h,
where V is the volume, π is a constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cone.
In your question, the volume of the cone is given as 100 cm^3 and the height is given as 12 cm. However, we don't have information about the radius, so we'll need to find that first.
By rearranging the formula above, we can solve for the radius:
r = √((3 * V) / (π * h)).
Plugging in the given values, we have:
r = √((3 * 100) / (π * 12)).
r = √(300 / (12π)).
r ≈ √7.957747.
Next, we can use the slant height, height, and radius to find the slant height.
The slant height, denoted as l, can be calculated using the Pythagorean theorem:
l = √(r^2 + h^2).
Plugging in the known values:
l = √(7.957747^2 + 12^2).
l ≈ 15.5649 cm.
Therefore, the slant height of the cone is approximately 15.5649 cm.