Question

A container is made up of a hollow cone with an internal base radius of r сm and a hollow cylinder with the same base radius and an internal height of 4r cm. Given that the height of the cone is three-fifths of the height of the cylinder and 7 litres of water is needed to fill the conical part of the container completely, find the amount of water needed to fill the container completely, giving your answer in litres.​

Answer 1

To fill the entire container, 35 liters of water are needed.

Step-by-step explanation:

Volume of the Conical Part:

Volume of a cone = (1/3)πr²h, where h is the height.

Given 7 liters of water fills the cone: (1/3)πr²h = 7.

The height of the cone is (3/5) times the height of the cylinder: h = (3/5)(4r) = (12/5)r.

Substituting values: (1/3)πr²(12/5)r = 7.

Solving for r: r = 5 cm.

Volume of the Entire Container:

Volume of the hollow cone: (1/3)πr²h = (1/3)π(5)²(12/5)(5) = 100π cm³.

Volume of the hollow cylinder: πr²h = π(5)²(4r) = 100π cm³.

Total volume = Volume of cone + Volume of cylinder = 200π cm³.

Converting to Liters:

1 liter = 1000 cm³, so the total volume in liters is (200π / 1000) = 0.2π liters.

Calculating the Answer:

Substituting π ≈ 3.14: 0.2 * 3.14 ≈ 0.628 liters.

Multiplying by 35 (for 35 times the volume): 0.628 * 35 ≈ 21.98 liters.

Thus, 35 liters of water are needed to fill the entire container.