Area of a Circle

Instruction Active

Finding Area from Circumference

The circumference of a circular pond in the park is 120 meters. Find the area

The formula for circumference is C = id

What is the value of the diameter rounded to the nearest whole number?

What is the value of the radius rounded to the nearest whole number?

The formula for area is = r2

What is the approximate area of the circular pond rounded to the nearest whole number?

m

The diameter of the pond is 38 m.

The radius of the pond is 19 m.

The area of the pond is 361 m^2.

Step-by-step explanation:

We know that the circumference C of a circle is equal to

In this case, C is equal to 120 m.

The diameter is then:

Rounded to the nearest whole number, the diameter is D=38 metres.

The radius is equal to half the diameter, so the radius of this pond is R=19 metres.

The area can be calculated from the radius as:

The area is 361 m^2

i) Diameter = 38 meters

ii) Radius = 19 meters

iii) Area = 361 m²

Step-by-step explanation:

i) According to the formula given in the question, the formula for the circumference, C = πD

C = 120 meters

Diameter, D = 120/π

D = 38 meters

ii) The value of the radius

Radius, r = (Diameter, D)/2

r = 38/2

r = 19 meters

iii) What is the approximate area

From the question, the expression for the area is A = r²

Area, A = 19²

A = 361 meters

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.