Question

Для покраски бассейна длиной 10 м,шириной 4м и глубиной 2м израсходовали 96кг краски.Сколько краски потребуется, если увеличить длину и ширину бассейна на 1м? Решить задачу.

Answer 1

Площадь покрытая 96 кг краски = 4*10+4*2+4*2+2*10+2*10=96 м кв
на 1 кв м расходуется 96/96=1 кг краски
Площадь нового бассейна = 11*5+5*2+5*2+11*2+11*2=119 м кв.
надо 119 кг краски

Answer 2

Problem Analysis

To solve this problem, we need to determine the amount of paint required to paint a pool with dimensions 10m in length, 4m in width, and 2m in depth. We are also asked to find the amount of paint required if the length and width of the pool are increased by 1m.

Solution

Let's start by calculating the volume of the pool using the given dimensions. The volume of a rectangular prism (such as a pool) is calculated by multiplying its length, width, and depth.

The initial volume of the pool is: Volume = Length x Width x Depth Volume = 10m x 4m x 2m Volume = 80 cubic meters

Next, we need to determine the amount of paint required to cover the pool. The amount of paint required depends on the surface area to be painted. To calculate the surface area, we need to find the area of each side of the pool and then sum them up.

The area of the bottom of the pool is: Area_bottom = Length x Width Area_bottom = 10m x 4m Area_bottom = 40 square meters

The area of each side of the pool is: Area_side = Length x Depth Area_side = 10m x 2m Area_side = 20 square meters

Since there are two sides, we multiply the area of one side by 2: Total_area_side = 2 x Area_side Total_area_side = 2 x 20 square meters Total_area_side = 40 square meters

The total surface area of the pool is the sum of the area of the bottom and the total area of the sides: Total_surface_area = Area_bottom + Total_area_side Total_surface_area = 40 square meters + 40 square meters Total_surface_area = 80 square meters

Now, we can calculate the amount of paint required to cover the pool. The amount of paint required is typically given in kilograms per square meter (kg/m^2). In this case, we are told that 96kg of paint was used to cover the pool.

To find the amount of paint required for the increased dimensions, we need to calculate the new surface area. Since both the length and width are increased by 1m, the new dimensions of the pool are 11m in length and 5m in width.

The new area of the bottom of the pool is: New_area_bottom = New_length x New_width New_area_bottom = 11m x 5m New_area_bottom = 55 square meters

The new area of each side of the pool is: New_area_side = New_length x Depth New_area_side = 11m x 2m New_area_side = 22 square meters

Since there are two sides, we multiply the area of one side by 2: New_total_area_side = 2 x New_area_side New_total_area_side = 2 x 22 square meters New_total_area_side = 44 square meters

The new total surface area of the pool is the sum of the new area of the bottom and the new total area of the sides: New_total_surface_area = New_area_bottom + New_total_area_side New_total_surface_area = 55 square meters + 44 square meters New_total_surface_area = 99 square meters

To find the amount of paint required for the increased dimensions, we can use the ratio of the new surface area to the initial surface area and multiply it by the initial amount of paint used.

Amount_of_paint_required = (New_total_surface_area / Total_surface_area) x Initial_amount_of_paint Amount_of_paint_required = (99 square meters / 80 square meters) x 96kg Amount_of_paint_required = 1.2375 x 96kg Amount_of_paint_required ≈ 118.8kg

Therefore, if the length and width of the pool are increased by 1m, approximately 118.8kg of paint will be required to cover the pool.

Answer

If the length and width of the pool are increased by 1m, approximately 118.8kg of paint will be required to cover the pool.