Question

Деревянный брус имеет форму прямоугольного параллелепипеда. Его длина 50 см, ширина на 10 см меньше длины, а высота в 2 раза меньше ширины. Сколько потребуется краски, чтобы покрасить поверхность бруска, если для покраски 1 дм2 поверхности нужно 4 грамма краски

Answer 1

2(ab+bc+ca)=S поверхности прямоугольного параллелепипеда, где a-длина, b - ширина, с -высота
1) 50-10=40 cм - ширина
2) 40:2=20 см - высота
3) 2(50*40+40*20+20*50)=2(2000+800+1000)=7600 кв см = 76 кв дм - площадь поверхности прямоугольного параллелепипеда
4) 76*4 = 304 г краски потребуется

Answer 2

Problem Analysis

We are given a wooden beam in the shape of a rectangular parallelepiped. The length of the beam is 50 cm, the width is 10 cm less than the length, and the height is 2 times less than the width. We need to calculate the amount of paint required to cover the surface of the beam, given that 4 grams of paint are needed to paint 1 square decimeter (dm²) of surface.

Calculation

To calculate the amount of paint required, we need to find the surface area of the beam and then multiply it by the amount of paint needed per square decimeter.

Let's calculate the dimensions of the beam: - Length = 50 cm - Width = Length - 10 cm = 50 cm - 10 cm = 40 cm - Height = Width / 2 = 40 cm / 2 = 20 cm

Now, let's calculate the surface area of the beam: - Surface area = 2 * (Length * Width + Length * Height + Width * Height)

Substituting the values: - Surface area = 2 * (50 cm * 40 cm + 50 cm * 20 cm + 40 cm * 20 cm)

Converting the dimensions to square decimeters (1 dm = 10 cm): - Surface area = 2 * (5 dm * 4 dm + 5 dm * 2 dm + 4 dm * 2 dm)

Simplifying the expression: - Surface area = 2 * (20 dm² + 10 dm² + 8 dm²) - Surface area = 2 * 38 dm² - Surface area = 76 dm²

Finally, let's calculate the amount of paint required: - Amount of paint = Surface area * 4 grams/dm² - Amount of paint = 76 dm² * 4 grams/dm²

Calculation Result

The amount of paint required to cover the surface of the wooden beam is 304 grams.

Answer

To paint the surface of the wooden beam, you will need approximately 304 grams of paint.