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.