An artist creates a cone-shaped sculpture for an art exhibit. If the sculptor is 5 feet tall and has a base with a circumference of 20.096 feet, what is the volume of the sculpture? Use 3.14 for pie

The volume of the sculpture is 53.589 ft³

Step-by-step explanation:

Here, we note that the volume of a right circular cone is given by

Where:

V = Volume of the right circular cone

r = Radius of the base of the cone

h = Height of the cone = 5 ft

π = Constant = 3.14

However, the circumference is given as

Circumference = 20.096 ft

The formula for circumference  is

Circumference  = 2πr

Therefore, 2πr = 20.096 ft and

Therefore,

.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).