A cone has a volume of 144π in3 and a diameter of 12 in. Wilson states that a cylinder with the same height and diameter has the same volume. Which statement explains whether or not Wilson is correct?
A cylinder in which h = 12 and d = 12 has a volume of 144π in3; therefore, Wilson is correct.
A cylinder in which h = 4 and d = 12 has a volume of 144π in3; therefore, Wilson is correct.
A cylinder in which h = 12 and d = 12 has a volume of 432π in3; therefore, Wilson is incorrect.
A cylinder in which h = 4 and d = 12 has a volume of 432π in3; therefore, Wilson is incorrect.

if the diameter of the cone is 12, then its radius is half that, or 6 units.

so a cylinder with a height of 12 and a diameter of 6 will have that volume, thus Wilson is incorrect.

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).