What is the slant height of a right cone with a diameter of 12 cm and a height of 15 cm?

Question

Hi I am felly stuck on the geometry question and I need help!

Answer 1

To find the slant of a cone, first identify variables

d = 12cm

d/2 = r = 6cm  this gets you the radius

h = 15cm
l = slant height = ?

 

Formula

l = square root(r² + h²)

Plug and Chug

l = square root(6² + 15²)

l = square root(36 + 225)

l = square root(261)

l ≈ 16.15549 cm

It might help you if you draw a cone and realize that the formula you just used is the Pythagorean Theorem (a² + b² = c²) but applied to cones. The "a" is your "r", the "b" is your "h", and the "c" is your "l".

Answer 2

slant height is the segment that is drawn from the top of the cone to the circumference of the base circle. It forms a right triangle  with the height  and radius of the circle being the legs and the slant height being the hypotenuse. So using the Pythagorean theorem, you would get 6^2 + 15^2 = c^2, and c=sqrt 261 which simplifies to 3*sqrt 29.