Uncle Bert was making porridge in a cylindrical pan of diameter 24cm. The spoon he was using is 26 cm long. It accidentally falls and sinks into the porridge. Calculate the minimum volume of porridge necessary to hide the spoon. You may ignore the volume of the spoon.
1. 5523.9cm3
2. 6525.9cm3
3. 4225.9cm3
4. 4525.9cm3
26^2-24^2 = 100
So, the porridge must be at least 10 cm deep.
The volume of porridge is thus at least 1440π = 4523.9 cm^3
hw did u get dis ??
The volume of porridge is thus at least 1440π
volume of a cylinder v = πr^2 h
They wouldn't be asking this kind of question if you hadn't learned that.
Now, how did I get a depth of 10 cm?
Draw a diagram of the pot and spoon, as seen from the side. The spoon is lying with one end on the bottom of the pot, and the other end leaning against the side of the pot.
Recall the Pythagorean Theorem. You have a right triangle with the spoon forming the hypotenuse, and the diameter of the bottom of the pot forming one leg. If the depth is d,
24^2 + d^2 = 26^2
d=10
Whenever you get one of these problems, it always pays to draw a diagram, and review what you have studied so far. The answer will come from using the topics covered; these are not just random problems pulled out of a hat.
To calculate the minimum volume of porridge necessary to hide the spoon, we need to consider the height of the spoon that is submerged in the porridge.
The spoon will be completely submerged when its length is greater than or equal to the height of the porridge.
First, let's find the height of the spoon submerged in the porridge:
Since the spoon falls into a cylindrical pan, we can assume that the porridge forms a cylindrical shape as well.
The diameter of the pan is 24 cm, which means the radius (r) of the pan is half of the diameter, so r = 24 cm / 2 = 12 cm.
Now we need to find the height (h) of the porridge. We can use the Pythagorean theorem to calculate this:
h^2 = (26 cm)^2 - (12 cm)^2
h^2 = 676 cm^2 - 144 cm^2
h^2 = 532 cm^2
h ≈ √532 cm
h ≈ 23.09 cm
So, the height of the porridge necessary to hide the spoon is approximately 23.09 cm.
Now, let's calculate the volume of the porridge using the formula for the volume of a cylinder:
V = π * r^2 * h
V ≈ 3.1416 * (12 cm)^2 * 23.09 cm
V ≈ 3.1416 * 144 cm^2 * 23.09 cm
V ≈ 31825.17 cm^3
Therefore, the minimum volume of porridge necessary to hide the spoon is approximately 31825.17 cm^3.
None of the answer choices provided match this volume. Please double-check the calculations or check if there are any other constraints given in the question.