Question

В сосуд цилиндрической формы налили воду до уровня 80 см. какого уровня достигнет вода , если ее перелить в другой цилиндрический сосуд, у которого радиус основания в 4 раза больше, чем у первого. Ответ в см

Answer 1

$h=80 \\ V_c= \pi R^2h=80 \pi R^2 \\ V_{new}= \pi (4R)^2H \\ V_c=V_{new}\\ 80 \pi R^2=\pi (4R)^2H \\ 80 \pi R^2= \pi 16R^2H \\ H= \frac{80 \pi R^2}{\pi 16R^2}= \frac{80}{16}=5\\ H=5$

Answer 2

Calculating the New Water Level in the Second Cylinder

To calculate the new water level in the second cylindrical vessel, we can use the principle that the volume of water remains constant when transferred from one vessel to another.

Given: - Initial water level in the first cylindrical vessel = 80 cm - The radius of the second cylindrical vessel is 4 times larger than the radius of the first one.

Calculation Steps

1. Calculate the Volume of Water in the First Cylinder: - The volume of water in a cylinder is given by the formula: V = πr^2h, where r is the radius and h is the height. - Using the initial water level (h = 80 cm) and the radius of the first cylinder, we can calculate the initial volume of water.

2. Calculate the New Height of Water in the Second Cylinder: - Since the volume of water remains constant, we can use the formula V = πr^2h to find the new height (h') in the second cylinder, using the new radius.

Calculation

1. Calculate the Volume of Water in the First Cylinder: - Using the initial water level (h = 80 cm) and the radius of the first cylinder, we can calculate the initial volume of water. - Let's assume the radius of the first cylinder is 'r' cm.

- The initial volume of water in the first cylinder is given by: V1 = πr^2 * 80 cm 2. Calculate the New Height of Water in the Second Cylinder: - Given that the radius of the second cylinder is 4 times larger than the radius of the first one, the radius of the second cylinder is 4r cm.

- Using the formula V = πr^2h, we can find the new height (h') in the second cylinder: V1 = V2 πr^2 * 80 = π(4r)^2 * h' Solving for h', we get: h' = (r^2 * 80) / (16r^2) h' = 5 cm

Conclusion

When the water is poured into the second cylindrical vessel with a radius 4 times larger than the first one, the water level will reach a height of 5 cm in the second vessel.