Aheavy metal sphere
with radius 10 cm is dropped into a rightcircular cylinder with
base radius of 10 cm. if the originalcylinder has water in it that
is 20 cm high, how high is the waterafter the sphere is placed in
it?

the height of the water after the sphere is placed in

it is 33.33 cm

Step-by-step explanation:

The cylinder is called a right circular cylinder because its height make a right angle with its base. The formula for determining the volume of the cylinder is expressed as

Volume = πr^2h

Where

π is a constant whose value is 3.14

r represents the radius of the cylinder.

h represents the height of the cylinder.

From the information given,

r = 10 cm

h = height of water in the cylinder = 20 cm

Volume of water in the cylinder before the sphere was placed in it would be

V = 3.14 × 10^2 × 20 = 6280 cm^3

The formula for determining the volume of the sphere is expressed as

Volume = 4/3 πr^3

V = 4/3 × 3.14 × 10^3 = 4186.67cm^3

Total volume of the sphere and the cylinder = 6280 + 4186.67 = 10466.67 cm^2

To determine the new height of the water,

10466.67 = 3.14 × 10^2× h

h = 10466.67/314 = 33.33 cm

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).