The national park has a new kiosk which visitors pass through as they enter the park. The kiosk is in the shape of a cylinder with a diameter of 5 meters and a height of 3 meters and a conical roof that measures 2 meters in height. What is the volume of the kiosk? Round your answer to the nearest cubic meter.

Given:

Kiosk is the combination of a cylinder and a cone.

Diameter of cylinder and cone = 5 m

Height of the cylinder = 3 m

Height of the cone = 2 m

To find:

The volume of the kiosk.

Solution:

We know that the radius is half of the diameter. So,

Radius of cylinder and cone = m

                                               = m

Volume of the cylinder is:

Where, r is the radius and h is the height of the cylinder.

Putting in the above formula, we get

Volume of a cone is:

Where, r is the radius and h is the height of the cone.

Putting in the above formula, we get

The volume of the kiosk is the sum of volume of cylinder and the volume of cone.

Therefore, the volume of the kiosk is 72 cubic meter.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

step-by-step explanation:

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