2. The base of a cylindrical juice container is a circle with diameter of 20 cm. The height of the container is 80 cm.
a) What is the volume of the juice container?
b) The juice container will be filled to 85% of its capacity. What will the volume of the juice in the container be?
a) The radius of the base of the container is half of the diameter, so it is 10 cm. The formula for the volume of a cylinder is V = πr^2h, where π is approximately 3.14, r is the radius, and h is the height. Substituting the given values, we get:
V = π(10 cm)^2(80 cm)
V = 25,120 cm^3
Therefore, the volume of the juice container is 25,120 cubic centimeters.
b) If the container is filled to 85% of its capacity, that means there is 15% of the capacity left empty. The volume of the empty space is 0.15 times the total volume of the container:
0.15 × 25,120 cm^3 = 3,768 cm^3
To find the volume of the juice in the container, we can subtract this empty volume from the total volume:
25,120 cm^3 - 3,768 cm^3 = 21,352 cm^3
Therefore, the volume of the juice in the container will be 21,352 cubic centimeters.
a) To find the volume of the juice container, we can use the formula for the volume of a cylinder which is given by V = πr^2h, where V is the volume, π is a constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the container.
Given that the diameter of the base is 20 cm, the radius can be found by dividing the diameter by 2. So, the radius (r) of the base is 20 cm / 2 = 10 cm.
Substituting the values into the formula:
V = πr^2h
V = π(10 cm)^2(80 cm)
Calculating the value:
V ≈ 3.14159 * 10 cm * 10 cm * 80 cm
V ≈ 31.4159 * 1000 cm^3
V ≈ 31,415.9 cm^3
Therefore, the volume of the juice container is approximately 31,415.9 cm^3.
b) The volume of the juice in the container when it is filled to 85% of its capacity can be found by multiplying the volume of the container by 0.85.
To calculate this:
Volume of the juice = 0.85 * Volume of the container
Volume of the juice = 0.85 * 31,415.9 cm^3
Calculating the value:
Volume of the juice ≈ 0.85 * 31,415.9 cm^3
Volume of the juice ≈ 26,703.5 cm^3
Therefore, the volume of the juice in the container when it is filled to 85% of its capacity is approximately 26,703.5 cm^3.
To find the volume of the juice container, we can use the formula for the volume of a cylinder:
V = πr^2h
where:
V is the volume,
π is a mathematical constant approximately equal to 3.14159,
r is the radius of the base of the cylinder,
h is the height of the cylinder.
First, let's find the radius of the base. The diameter of the circle is given as 20 cm, which means the radius is half of that:
r = 20 cm / 2 = 10 cm
a) Now we can calculate the volume of the juice container:
V = π(10 cm)^2 * 80 cm
= π * 100 cm^2 * 80 cm
= 8000π cm^3
b) To find the volume of the juice when it's filled to 85% of the capacity, we need to multiply the volume of the container by 85% or 0.85:
Volume of the juice = 0.85 * 8000π cm^3
= 6800π cm^3
Therefore, the volume of the juice in the container will be 6800π cm^3.