Question

Calculate the slant height for the given cone? . round to the nearest tenth

Answer 1

It should be the third answer choice.

Explanation:

Since the slant height is the hypotenuse of the orange triangle, we can use the Pythagorean theorem to find out what the height is. The squares of the two legs added together should equal the square of the hypotenuse.

The two legs are 9 cm and 4 cm. The height of the triangle is shown to be the same as the height of the cone. The triangle is also shown to have a base that is half of the cone's diameter (8 divided by 2).

Plug these numbers into the Pythagorean theorem:

`4^2+9^2`

`16+81`

`97`

That means the square of the hypotenuse (the cone's slant height) is `sqrt97`.

That is approximately equal to 9.8488578018

Answer 2

Slant height `color(green)(l = 9.8` `color(brown)(cm)`

Explanation:

consider the shaded right triangle.

r is the base, h is the height and l the slant height.
Applying pythagorean theorem,

`l^2 = r^2 + h^2`

Given : # r = d/2 = 8/2 = 4 cm, h = 9 cm

Therefore, slant height `l = sqrt(4^2 + 9^2) = sqrt(97) ~~ color(green)(9.8 cm)`

corrected to one decimal