Question

Довжина акваріума який має форму прямокутного паралелепіпеда дорівнює 5 дм,ширина 4 дм. Коли в акваріум налили 48 л. води то він наповнився на 4/5 його об'єму. Знайти висоту акваріума

Answer 1

48*5:4=60 (л) об*єм акваріума
5*4=20 (дм²) площа дна
60:20=3 (дм) висота акваріума
Відповідь: 3 дм.

Answer 2

48 л = 48 дм³ 
1) 48 : (5/4) = 12*5 = 60 (дм³) - весь объем аквариума

V = Sh, S - площадь дна, h - высота
h = V/S

2) 4 * 5 = 20 (дм²) - площадь дна
3) 60 : 20 = 3 (дм) - высота

Ответ: 3 дм

Answer 3

Calculation of the Height of the Aquarium

To find the height of the aquarium, we can use the formula for the volume of a rectangular parallelepiped:

Volume = Length x Width x Height

Given that the length of the aquarium is 5 dm and the width is 4 dm, we can substitute these values into the formula:

Volume = 5 dm x 4 dm x Height

We also know that when 48 liters of water were poured into the aquarium, it was filled to 4/5 of its volume. This means that the volume of water in the aquarium is equal to 4/5 of the total volume of the aquarium.

Let's denote the height of the aquarium as 'h'. The volume of water in the aquarium can be calculated using the formula:

Volume of water = Length x Width x Height of water = 48 liters

Since the volume of water is equal to 4/5 of the total volume of the aquarium, we can write the equation:

(4/5) x (Length x Width x Height) = 48 liters

Substituting the given values for length and width, we have:

(4/5) x (5 dm x 4 dm x h) = 48 liters

Simplifying the equation, we can cancel out the units of dm:

(4/5) x (20h) = 48

Now, let's solve for 'h':

(4/5) x 20h = 48

Multiplying both sides by 5/4 to isolate 'h', we get:

20h = (48 x 5/4)

Simplifying further:

20h = 60

Dividing both sides by 20, we find:

h = 60/20 = 3 dm

Therefore, the height of the aquarium is 3 dm.