To find the height of the cylinder, we need to find the distance between points N and Q, which is twice the length of the radius of circle Q.
Given that the circumference of the cylinder is 145cm, we can use the formula for the circumference of a circle:
Circumference = 2πr
Where r is the radius of the circle.
Given that the circumference is 145cm, we have:
145 = 2πr
Solving for r:
r = 145 / (2π) ≈ 23.08 cm
Since the distance between points N and Q is twice the length of the radius of circle Q, the height of the cylinder would be:
Height = 2 * 23.08 = 46.16 cm
Now, to find the volume of the cylinder, we use the formula for the volume of a cylinder:
Volume = πr^2h
Where r is the radius and h is the height of the cylinder.
Substitute the values:
Volume = π(23.08)^2 * 46.16
Volume ≈ 39863.2 cm^3
Therefore, the height of the cylinder is 46.16 cm and the volume of the cylinder is approximately 39863.2 cm^3.
1. In the figure below, all of the following statements are true: a. The top face of the cylinder is a circle with the point Q as its center.
b. Point N lies on the edge of the cylinder's base.
c. The distance between points N and Q is twice the length of the radius of circle Q. d. If the circumference of the cylinder is 145cm, then what is the height of the cylinder?
e. What is the volume of the cylinder? Show your work for full marks [
1 answer