Final answer:
A cone has a slant length of 5 and a diameter of 6.525 cubic units. Thus, no correct option was given.
Step-by-step explanation:
To calculate the volume of a cone, we can use the formula V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone. In this case, the slant length is given, but we need the radius. The slant length, also known as the slant height, is the hypotenuse of a right triangle formed by the slant height, the radius, and the height of the cone.
To find the radius, we can use the Pythagorean theorem: r = √(slant length² - height²). Given that the slant length is 5 and the diameter is twice the radius, we can calculate the radius as follows:
r = √(5² - (d/2)²)
Since the diameter is twice the radius, we can substitute
r = √(5² - (2r)²)
4r² = 5²
r = 5/2 = 2.5
Now we can calculate the volume using the formula V = (1/3)πr²h. Plugging in the values, we have
V = (1/3)π(2.5)²h
= (1/3)π(6.25)h
= 2.08πh
Since the value of π is approximately 3.142:
2.08 x 3.142 ≈ 6.525 cubic units.
Thus, there is no correct option.