contestada

Tank X and Tank Y altogether contains some amount of water. The height of the water in both the tanks are equal.
Tank Y was
filled with water.
When all the water from Tank Y was poured into Tank X, 4 litres of water overflowed. Tank Y’s base was 48cm and its length was 25cm. Tank X’s base was 50cm and its length was 40cm. (a) Find the total amount of water in both tanks. (b) Find the total capacity of Tank Y

Respuesta :

Let's denote:
- \( h \) as the height of the water in both tanks.
- \( V_X \) as the volume of water in Tank X.
- \( V_Y \) as the volume of water in Tank Y.

Given that the height of water in both tanks is equal, and when all the water from Tank Y is poured into Tank X, 4 liters of water overflow, we can set up the equation:

\[ V_X + V_Y - 4 = V_X + V_Y \]

Solving for \( V_Y \), we get:

\[ V_Y = 4 \, \text{liters} \]

Now, to find the total amount of water in both tanks (\( V_X + V_Y \)), we need to find \( V_X \). We'll use the formula for the volume of a rectangular tank:

\[ V = \text{base area} \times \text{height} \]

For Tank Y:
\[ V_Y = \text{base area}_Y \times h \]
\[ 4 = (48 \times 25) \times h \]
\[ h = \frac{4}{1200} \]
\[ h = \frac{1}{300} \]

Now, for Tank X:
\[ V_X = \text{base area}_X \times h \]
\[ V_X = (50 \times 40) \times \frac{1}{300} \]
\[ V_X = \frac{1}{3} \]

So, the total amount of water in both tanks is \( V_X + V_Y = \frac{1}{3} + 4 = \frac{13}{3} \) liters.

Now, to find the total capacity of Tank Y, we use the formula for the volume of a rectangular tank:

\[ \text{Volume}_Y = \text{base area}_Y \times \text{height} \]
\[ \text{Volume}_Y = (48 \times 25) \times \frac{1}{300} \]
\[ \text{Volume}_Y = 4 \]

Therefore, the total capacity of Tank Y is 4 liters.

Otras preguntas