The volume of an oblique cone with equal diameter and height is 18pi cm^3. Find the height and radius(to the nearest cm).
recall that the volume of an oblique cone is given by
V = (1/3)*(πr^2)*h
where
r = radius of circle (the base)
h = height
since diameter is equal to the height, we can say that
h = d = 2r
substituting,
V = (1/3)π(r^2)(2r)
18π = (2/3)π(r^3)
18*(3/2) = r^3
27 = r^3
r = 3 cm
h = 6 cm
hope this helps~ :)
To find the height and radius of the oblique cone, we can use the formula for the volume of a cone:
V = (1/3) * π * r^2 * h
Given that the volume is 18π cm^3 and the diameter and height are equal, we can express this in terms of the radius:
18π = (1/3) * π * r^2 * h
Divide both sides of the equation by π:
18 = (1/3) * r^2 * h
Multiply both sides of the equation by 3:
54 = r^2 * h
Since the diameter and height of the cone are equal, we can express the height in terms of the radius:
h = 2r
Substituting this into the equation:
54 = r^2 * 2r
Simplifying:
54 = 2r^3
Divide both sides of the equation by 2:
27 = r^3
Taking the cube root of both sides, we find:
r ≈ 3 cm
Substituting this value back into the equation for h:
h = 2r = 2 * 3 = 6 cm
Therefore, the approximate height is 6 cm and the approximate radius is 3 cm.
To find the height and radius of an oblique cone, we need to use the formula for the volume of a cone and set it equal to the given value.
The formula for the volume of a cone is given by:
V = (1/3) * π * r^2 * h,
where V is the volume, π is pi (approximately 3.14159), r is the radius of the base, and h is the height of the cone.
Given that the volume of the cone is 18π cm^3, we can plug this value into the volume formula and solve for r and h.
18π = (1/3) * π * r^2 * h (since V = 18π)
We can simplify the equation by canceling out the π on both sides:
18 = (1/3) * r^2 * h
Next, since the diameter and height of the cone are equal, we can substitute h with r in the equation:
18 = (1/3) * r^2 * r
Simplifying further:
54 = r^3
Take the cubic root of both sides:
∛54 = ∛r^3
∛54 = r
Now, we can calculate the value of r:
r ≈ 3.78 cm (rounded to two decimal places)
Since the diameter and height are equal, the height of the cone will also be approximately equal to 3.78 cm:
h ≈ 3.78 cm (rounded to two decimal places)
Therefore, the height and radius (to the nearest cm) of the oblique cone are approximately 3.78 cm.