the lateral area of a cone with radius 4 cm is 60 cm. a) Determine the slant height of the cone? b) Determine the height of the cone.
+130478 the lateral area of a cone with radius 4 cm is 60 cm. a) Determine the slant height of the cone? b) Determine the height of the cone.
----------------------------------------------------------------------------------------------------------------------------
The "formula" for the lateral surface area of a cone is given by:
A = π * r * l
Where A is the area, r is the radius, and l is the slant height. For convenience, I'll use 3.14 for π. So we have....
60 = 3.14 * 4 * l Solving for l, we have....
(60)/(3.13 * 4) = l ≈ 4.77 cm.
Now, to find the height, we can note that the height and the radius form two legs of a right triangle, and the slant height, l, forms the hypoteneuse. Something like this:
So we have, using the Pythagorean Throrem, h = SQRT( l2 - r2)
So we have:
h = SQRT(4.772 - 42) ≈ 2.6 cm.
That makes sense. It should be less than the hypoteneuse.....and it is!! It's always good to check that your answer is "reasonable!!" Also note, that it's a pretty "flat" cone!!!
+130478 the lateral area of a cone with radius 4 cm is 60 cm. a) Determine the slant height of the cone? b) Determine the height of the cone.
----------------------------------------------------------------------------------------------------------------------------
The "formula" for the lateral surface area of a cone is given by:
A = π * r * l
Where A is the area, r is the radius, and l is the slant height. For convenience, I'll use 3.14 for π. So we have....
60 = 3.14 * 4 * l Solving for l, we have....
(60)/(3.13 * 4) = l ≈ 4.77 cm.
Now, to find the height, we can note that the height and the radius form two legs of a right triangle, and the slant height, l, forms the hypoteneuse. Something like this:
So we have, using the Pythagorean Throrem, h = SQRT( l2 - r2)
So we have:
h = SQRT(4.772 - 42) ≈ 2.6 cm.
That makes sense. It should be less than the hypoteneuse.....and it is!! It's always good to check that your answer is "reasonable!!" Also note, that it's a pretty "flat" cone!!!
