Question

В парке поставили декоративный объект в форме шара и решили покрасить поверхность золотистой краской. Сколько килограммов краски необходимо, если на один квадратный метр уйдёт 200 граммов краски? Радиус сферы равен 134 см. Значение числа π≈3,14. Определи площадь поверхности S этой сферы (с точностью до сотых) в м² и необходимое количество краски, округляя до целых кг (в большую сторону).

Answer 1

S= πR²

134 см = 1,34 м

S= 3,14 * 1,34²

S≈ 5,64 м²

5,64 * 200 = 1128 (г)

1128 г ≈ 1 кг

ответ : 5,64 м² ; 1 кг краски

Answer 2

Calculating Surface Area of the Sphere

To determine the amount of paint needed, we first need to calculate the surface area of the sphere.

The formula for the surface area of a sphere is given by: S = 4πr^2

Where: - S = surface area - π (pi) is approximately 3.14 - r = radius of the sphere

Substituting the given radius of 134 cm into the formula: S = 4 * 3.14 * (134 cm)^2

Calculating the surface area: S ≈ 4 * 3.14 * 17956 cm² S ≈ 22543.84 cm²

Converting the surface area to square meters: S ≈ 22543.84 cm² ÷ 10000 S ≈ 2.2544 m²

So, the surface area of the sphere is approximately 2.2544 m².

Calculating the Amount of Paint Needed

Given that 200 grams of paint are needed for 1 square meter, we can calculate the total amount of paint required for the entire surface of the sphere.

Multiplying the surface area by the paint requirement per square meter: Total paint needed = 2.2544 m² * 200 g/m² Total paint needed ≈ 450.88 g

Converting the total paint needed to kilograms, rounding up to the nearest whole kilogram: Total paint needed ≈ 451 g

Therefore, approximately 451 kilograms of paint are needed to cover the entire surface of the sphere with a gold paint, rounding up to the nearest whole kilogram.