Answer:
question 18. the height of the cylinder is approximately 8.45 cm.
question 19. the height of the cylinder is 5 cm, the volume of the cylinder is approximately 98.17 cm^3.
I dont know how to do question 20, sorry.
question 18 explanation
The formula for the volume of a cylinder is:
V = πr^2h
where V is the volume, r is the radius of the base, and h is the height.
We are given that the volume is 6000 cm^3 and the diameter (which is twice the radius) of the base is 30 cm. Therefore, the radius of the base is:
r = d/2 = 30/2 = 15 cm
Substituting the given values into the formula for the volume, we get:
6000 cm^3 = π(15 cm)^2h
Simplifying the equation, we get:
6000 cm^3 = 225πh
Dividing both sides by 225π, we get:
h = 6000 cm^3 / (225π) ≈ 8.45 cm
Therefore, the height of the cylinder is approximately 8.45 cm.
question 19 explanation
If a cylinder has the same height as its width, it means that the diameter (which is twice the radius) of the base is equal to the height. Let's choose a value for the height, for example, let's say the height is 5 cm.
Then, the diameter of the base is also 5 cm, and the radius is:
r = d/2 = 5/2 = 2.5 cm
The formula for the volume of a cylinder is:
V = πr^2h
Substituting the given values, we get:
V = π(2.5 cm)^2(5 cm) = 31.25π cm^3 ≈ 98.17 cm^3
Therefore, if the height of the cylinder is 5 cm, the volume of the cylinder is approximately 98.17 cm^3.