Answer:
27 : 1
Step-by-step explanation:
The faces of a regular tetrahedron are equilateral triangles. The incenter, circumcenter, and centroid are all the same point, located 1/3 of the distance from the edge to the opposite vertex of the face. The vertical height of the point that is 1/3 the slant height from the base is 1/3 of the height of the tetrahedron.
Then the "inscribed" tetrahedron has 1/3 the height of the original. The ratio of volumes is the cube of the ratio of linear dimensions, so the ratio of the larger volume to the smaller is ...
3³ : 1³ = 27 : 1
Median is the number in the middle when all the numbers are put in order.
Let's do that first.
30 52 61 65 68 68 69 75 78 85
Now if there's 10 numbers, 2 numbers are in the middle.
By counting in 4 on both sides, we know the two numbers are both 68, so 68 is the median.
Answer:
339π in³
Step-by-step explanation:
The amount of water is the difference between the volume of the cylinder and the volume of the ball. The appropriate volume formulas are ...
cylinder V = πr²h
sphere V = (4/3)πr³
For the given numbers, the volumes are ...
cylinder V = π(5 in)²(15 in) = 375π in³
sphere V = (4/3)π(3 in)³ = 36π in³
The water volume is the difference of these ...
water volume = cylinder V - sphere V
= 375π in³ - 36π in³ = 339π in³