A cylindrical container of 15cm and depth of 20cm is full of water.If the water is poured into a empty cylinder jar of 10cm in diameter.Find the depth of the jar
the volume of water is v = πr^2 h = π*(15/2)^2 * 20 cm^3
so the depth is v/(25π) = 45 cm
44.99
To find the depth of the empty cylinder jar, we need to make use of the principle of the volume of a cylinder. The volume of a cylinder can be calculated using the formula:
Volume = π * r^2 * h
where π is a mathematical constant approximately equal to 3.14159, r is the radius of the cylinder's base, and h is the height or depth of the cylinder.
Given the dimensions of the initial cylindrical container (15 cm diameter, 20 cm depth) and the empty cylinder jar (10 cm diameter), we can find the depth of the jar by equating the volume of water in the full container to the volume of the empty jar.
1. Calculate the radius of the full cylindrical container:
The diameter of the container is 15 cm, so the radius (r1) can be found by dividing the diameter by 2:
r1 = 15 cm / 2 = 7.5 cm.
2. Calculate the volume of water in the full cylindrical container:
The volume of the full container is given by the formula:
Volume1 = π * r1^2 * h1,
where h1 is the depth of the full container, which is 20 cm.
3. Calculate the radius of the empty cylinder jar:
The diameter of the jar is 10 cm, so the radius (r2) can be found by dividing the diameter by 2:
r2 = 10 cm / 2 = 5 cm.
4. Equate the volume of water in the full cylindrical container to the volume of the empty jar:
Volume1 = Volume2,
where Volume2 is the volume of the empty jar.
Substituting the values we have:
π * r1^2 * h1 = π * r2^2 * h2,
or
(7.5 cm)^2 * 20 cm = (5 cm)^2 * h2.
5. Solve for the depth of the empty jar:
Divide both sides by (5 cm)^2:
h2 = ((7.5 cm)^2 * 20 cm) / (5 cm)^2.
Calculate the right-hand side of the equation to find the depth of the empty jar.
So, following these steps, you can find the depth of the empty cylinder jar.