The vertical angle of a cone is 70° and its height is 11cm. Calculate the slant height of the cone ( correct to the nearest whole number).
draw a diagram and review your basic trig functions. It should be clear that the slant height s can be found using
11/s = sin70°
To find the slant height of the cone, we can use trigonometry.
The slant height (l) can be found using the formula:
l = h / sin(angle)
where h is the height of the cone and angle is the vertical angle.
Given that the height of the cone (h) is 11 cm and the vertical angle is 70°, we can substitute these values into the formula:
l = 11 cm / sin(70°)
Using a scientific calculator to evaluate sin(70°), we get:
l ≈ 11 cm / 0.9397
Dividing 11 cm by 0.9397, we find:
l ≈ 11.71 cm
Therefore, the slant height of the cone, rounded to the nearest whole number, is approximately 12 cm.
To calculate the slant height of the cone, we can use the formula for the slant height of a cone in terms of the vertical angle and height. The formula is:
Slant height = Height / sin(vertical angle)
Given that the vertical angle is 70° and the height is 11cm, we can substitute these values into the formula:
Slant height = 11cm / sin(70°)
To find the value of sin(70°), we can use a scientific calculator or an online trigonometric calculator.
sin(70°) ≈ 0.9397
Substituting this back into the formula, we get:
Slant height = 11cm / 0.9397
Slant height ≈ 11.71cm
Rounding this to the nearest whole number, the slant height of the cone is approximately 12cm.
So the slant height of the cone, to the nearest whole number, is 12 cm.