Naulluq is cutting ice blocks from the lake for her mothers drinking water tank. The cylindrical tank has a volume of 4x^2π. Once each block has melted, it will have a volume of 3x^2. How many blocks does she need to cut so that her mothers tank will be filled when the ice melts? Give your answer to the nearest whole block.
(4πx^2)/(3x^2) = 4π/3 = 4.19
To find the number of blocks Naulluq needs to cut, we need to determine the volume of each ice block and divide it into the volume of her mother's tank.
The volume of a cylinder is given by the formula: V = πr^2h
In this case, we know that the volume of Naulluq's mother's tank is 4x^2π, so we can equate the two volumes:
4x^2π = πr^2h
Simplify by canceling out π:
4x^2 = r^2h
We also know that the volume of each ice block, once melted, is 3x^2. So, we can equate the two volumes again:
3x^2 = πr^2h
Since both equations are equal to r^2h, we can equate them and solve for the ratio:
4x^2 = 3x^2
Subtract 3x^2 from both sides:
x^2 = 0
This equation doesn't have a solution, which means we cannot fill the tank with the given ice block volume.
Therefore, Naulluq cannot fill her mother's tank with the ice blocks available.
To find out how many blocks Naulluq needs to cut, we need to compare the volume of the cylindrical tank to the volume of each ice block after it melts.
The volume of the cylindrical tank is given as 4x^2π.
The volume of each ice block after melting is given as 3x^2.
To find out how many blocks are needed, we can set up the equation:
Number of blocks = Volume of tank / Volume of each block
Plugging in the given values, we have:
Number of blocks = (4x^2π) / (3x^2)
We simplify this expression:
Number of blocks = (4/3) * π
Now we can calculate the approximate number of blocks needed. Let's use the value of π as 3.14159:
Number of blocks = (4/3) * 3.14159
Number of blocks ≈ 4.18879
Rounding to the nearest whole block, Naulluq needs to cut 4 blocks so that her mother's tank will be filled when the ice melts.