Question

A cylindrical container has a radius of 3 centimeters and a height of 12 centimeters. The container is filled with water up to the height of 7 centimeters. Find the volume of empty space in the cylinder.

Answer 1

The volume of the empty space in the cylinder is equal to the difference between the volume of the cylinder and the volume of water in the cylinder.

The volume of the cylinder can be calculated using the formula:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

Substituting the given values, we get:

V = π(3 cm)^2(12 cm)

V ≈ 339.3 cubic centimeters

The volume of water in the cylinder can be calculated by multiplying the cross-sectional area of the cylinder by the height of the water:

V_water = πr^2h_water

where V_water is the volume of water and h_water is the height of the water.

Substituting the given values, we get:

V_water = π(3 cm)^2(7 cm)

V_water ≈ 197.9 cubic centimeters

Therefore, the volume of empty space in the cylinder is:

V_empty = V - V_water

V_empty ≈ 339.3 - 197.9

V_empty ≈ 141.4 cubic centimeters

So, the volume of empty space in the cylinder is approximately 141.4 cubic centimeters.

Answer 2

volume of empty space = 141.3 cm³

Explanation:

volume of empty space = volume of the cylinder - volume of water

First, we need to calculate the volume of the container

volume of a cylinder = πr²h

where r = radius of the container and h is the height of the container

r = 3cm and h = 12 cm π is a constant which is ≈ 3.14

volume of a cylinder = πr²h

=3.14 × 3²×12

=3.14×9×12

=339.12 cm³

We will proceed to find the volume of water

since liquid will take the shape of its container,

then volume of water = πr²h

r is the radius of the container and h is the height of the water

r = 3cm and h = 7cm

volume of water = πr²h

= 3.14 ×3²×7

=3.14×9×7

=197.82 cm³

volume of empty space = volume of the cylinder - volume of water

=339.12 cm³ - 197.82 cm³

= 141.3 cm³

OR

WE CAN SOLVE DIRECTLY

height of empty space = height of container - height of water

= 12 - 7

=5 cm

volume of empty space = πr²h

=3.14×3²×5

=3.14×9×5

=141.3 cm³

volume of empty space = 141.3 cm³