You will need
- the formula for the surface area of the balloon;
- - the formula for the volume of a sphere;
- - skills of arithmetic accounts.
In everyday life it is often necessary to calculate the area of the ball surface or part thereof to calculate, for example, the consumption of material. Calculating the volume of a ball, you can using specific gravity to calculate the mass of matter forming the contents of the sphere. To find the area and volume of the ballenough to know its radius or diameter. The formulas that the students of today derive in the 11th grade of secondary school, you can easily estimate these parameters.
For example, the diameter of a soccer ball, according to the FIFA requirements, must be in the range of 21.8 to 22.2 cm Average for ease of account up to 22 cm Therefore, radius (R) is equal to (22:2) – 11 cm it's interesting to know what the area of the surface of a soccer ball?
Take the formula of the surface area of the ball: Sof the ball = 4ттR2Подставьте in the above formula the value of the radius of a soccer ball is 11 cm S = 4 x 3.14 x 11x11 .
After carrying out simple mathematical operations, you get the result: 1519.76. Thus, the area of the surface of a soccer ball is 1 519.76 square centimeters.
Now calculate the volume of the ball. Take the formula for calculating the volume of a ball: V = 4/3ттR3Подставляйте again, the value of the radius of a soccer ball is 11 cm V = 4/3 x 3.14 x 11 x 11 x 11.
After counting, for example, on a calculator you get: 5576.89.It turns out that the volume of air in a football is 5 576.89 cubic centimeters.
Interesting: the volume of a sphere with a diameter in excess of three times the diameter of another ball, more of the total volume of three such balls 9 times.
To develop in children a passion for math calculations, offer examples for the calculation of the surrounding objects: the ball, watermelon, tangle grandmother's yarn. This is clearly because interested.
Advice 2: How to find the area, knowing the diameter
Objectives to calculate the area of a circle often meet in the school geometry course. To find the area of a circle, you need to know the length of the diameter or radius of a circle in which it is enclosed.
You will need
- - the length of the diameter of the circle.
A circle is a figure in the plane consisting of a plurality of points disposed in the same distance from another point called the centre. A circle is a flat geometric figure, represents the set of points enclosed in a circle which is the boundary of the circle. Diameter is a segment that connects two points on the circle and passing through its center. The radius is the segment connecting a point on the circle and its center. π — the number "PI", a mathematical constant that is the constant. It shows the ratio of the circumference to the length of its diameter. To compute the exact value of π is impossible. In geometry use the approximate value of this number: π ≈ 3,14
The area of a circle equals the product of the square of the radius to the number calculated by the formula: S=NR^2, where S is the area of the circle, R is the length of the radius of the circle.
From the definition of the radius, it follows that it is equal to half the diameter. Hence, the formula becomes: S=π(D/2)^2, where D is the length of the diameter of the circle. Substitute in the formula the value of the diameter, calculate the area of a circle.
The area of a circle is measured in square units — mm2, cm2, m2, etc. In what units is expressed you received the area of a circle depends on what units was the diameter of a circle.
If you need to calculate the area of a ring use this formula: S=π(R-R)^2, where R, r are radii of the outer and inner circumferences of the ring, respectively.
There is an international day of "PI", which is celebrated on March 14. The exact time of onset of the official date — 1 hour 59 minutes 26 seconds, according to figures the number is 3,1415926...