A cone has a slant length of 5 and a diameter of 4. What is the volume of the cone? Use π ≈ 3.14.
A.12.56 cubic units
B.18.84 cubic units
C.20.93 cubic units
D.25.12 cubic units

V = 19.19 cubic units

None of the options are correct.

Step-by-step explanation:

Volume of a cone is given as;

V = ⅓πr²h

Now, we are given;

diameter = 4 units

Thus radius;r = diameter/2 = 4/2 = 2 units

I have attached an image to show the diagram of the cone.

Now, to find the height (h), we know the radius(r) and we know the slant length(l) . So we can use Pythagoras theorem to find the height.

From Pythagoras theorem;

r² + h² = l²

Where l is the hypotenuse or the slant side while "r" is the radius of the cone while the height will be "h"

Thus;

2² + h² = 5²

h² = 5² - 2²

h² = 25 - 4

h² = 21

h = √21

h = 4.5826 units

So height (h) = 4.5826 units

Volume of cone;V = ⅓πr²h

We are told that π = 3.14

Thus;

V = ⅓ x 3.14 x 2² x 4.5826

V = 19.19 cubic units

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