The lateral area of a cone is 736 pi cm^2. The radius is 46 cm. Find the slant height to the nearest tenth.
A. 16 cm
B. 21.1 cm
C. 13.4 cm
D. 21.6 cm
step-by-step
a = πrs, so
46πs = 736π
s = 16
thanks! I figured i out though lol
To find the slant height of a cone with a given lateral area and radius, we can use the formula:
Lateral Area = π × radius × slant height
Given that the lateral area is 736π cm^2 and the radius is 46 cm, we can substitute these values into the formula:
736π = π × 46 × slant height
Dividing both sides of the equation by π × 46 gives:
slant height = 736π / (π × 46)
Cancelling out the π on the numerator and denominator, we get:
slant height = 736 / 46
Evaluating this expression, we find:
slant height = 16
Therefore, the slant height is 16 cm.
So the answer is A. 16 cm.
To find the slant height of a cone, we can use the Pythagorean theorem. The lateral area of a cone is given by the formula L = πrs, where L is the lateral area, π is pi, r is the radius, and s is the slant height.
Given that the lateral area is 736π cm^2 and the radius is 46 cm, we can substitute these values into the formula to solve for the slant height.
736π = π(46)(s)
Cancel out the π on both sides.
736 = 46s
Divide both sides by 46.
s = 736/46
s ≈ 16
Therefore, the slant height is approximately 16 cm.
The nearest option to 16 cm is A. 16 cm.