An inverted cone with base radius 77 cmcm and height 2121 cmcm is full of water. The water in this inverted cone is poured into a tall cylinder whose horizontal base has a radius of 77 cmcm. What is the height, in centimeters, of the water in the cylinder?
Question
An inverted cone with base radius 77 cmcm and height 2121 cmcm is full of water. The water in this inverted cone is poured into a tall cylinder whose horizontal base has a radius of 77 cmcm. What is the height, in centimeters, of the water in the cylinder?
Solution
First, we need to find the volume of the water in the cone. The formula for the volume of a cone is (1/3)πr²h, where r is the radius and h is the height.
So, the volume of the water in the cone is (1/3)π*(77 cm)²*(21 cm) = 166,924 cubic cm.
Next, we need to find the height of the water in the cylinder. The formula for the volume of a cylinder is πr²h. We know the volume of the water and the radius of the cylinder, so we can solve for the height.
So, 166,924 cubic cm = π*(77 cm)²*h.
Solving for h, we get h = 166,924 cubic cm / (π*(77 cm)²) = 7 cm.
So, the height of the water in the cylinder is 7 cm.
Similar Questions
A container is in the shape of a right circular cylinder standing on its base. If 100 cubic centimeters of water is poured into the container, the height of the water is 8 centimeters. What is the height of the water if only 75 cubic centimeters is poured into the container?
The solids below have the same base and the same height. If the cone is filled with water and poured into the cylinder, how much of the cylinder will be filled?Group of answer choices1/31/22/33/4
A graduated cylinder is filled with cm of liquid. The liquid is poured into a different cylinder that has a radius of cm.What will the height of the liquid be in the new cylinder?
A right circular cone of diameter k cm and height 12cm rests on the base of a rightcircular cylinder of radius k cm (their base lie in the same plane, as shown). Thecylinder is filled with water to a height of 12cm. If the cone is then removed, the heightto which the water will fall is
A cylinder with a radius of 1 cm and a height of 21 cm has the same volume as a cone with a height of 7 cm. What is the radius of the cone?ResponsesA 3 cm3 cmB 5 cm5 cmC 7 cm7 cmD 9 cm
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.