Question

find the volume of the cone below. as you can see the question is already answered my teacher wants me to show how she got the answer.

Answer 1

Question:

Solution:

The volume of the cone with radius r and height h is given by the following formula:

`V\text{ = }(1)/(3)\pi r^2h`

The data given in the problem are:

Diameter : 17.6 cm, then the radius is 17.6cm / 2 = 8.8 cm

Slant height : 25 cm

Thus, to find the height of the cone we use the Pythagorean theorem:

`h=\text{ }\sqrt[]{25^2-8.8^2}\text{ = 23.4}`

then we have that the given cone has a height of 23.4 cm and a radius of 8.8cm. So that, replacing these that into the first equation (volume of the cone), we get:

`V\text{ = }(1)/(3)\pi(8.8)^2(23.4)\text{ = }1897.6`

then, we can conclude that the correct answer is:

`V\text{ = }1897.6`