Question

the area of the base of a cylinder is calculated by:
a. ( 2pi rh )
b. ( \frac{4}{3}pi r^{3} )
c. ( 2pi r )
d. ( pi r^{2} )
what measurement do you need to calculate the volume of a cylinder?
a. diameter
b. circumference
c. radius
d. surface area

Explanation:

First Question

Step1: Recall the formula for the area of a circle (base of a cylinder)

The base of a cylinder is a circle. The formula for the area of a circle is \(A = \pi r^{2}\), where \(r\) is the radius of the circle.

• Option a: \(2\pi rh\) is the formula for the lateral (curved) surface area of a cylinder.
• Option b: \(\frac{4}{3}\pi r^{3}\) is the formula for the volume of a sphere.
• Option c: \(2\pi r\) is the formula for the circumference of a circle.
• Option d: \(\pi r^{2}\) is the formula for the area of a circle (base of a cylinder).

Second Question

Step1: Recall the formula for the volume of a cylinder

The formula for the volume of a cylinder is \(V=\pi r^{2}h\), where \(r\) is the radius of the base and \(h\) is the height of the cylinder.

• Option a: While diameter \(d = 2r\) (so radius \(r=\frac{d}{2}\)), the direct measurement needed in the formula is radius.
• Option b: Circumference \(C = 2\pi r\) (so \(r=\frac{C}{2\pi}\)), but the formula for volume uses radius directly.
• Option c: Since \(V=\pi r^{2}h\), radius \(r\) is needed.
• Option d: Surface area is not used in the formula \(V=\pi r^{2}h\) for the volume of a cylinder.

Answer:

1. d. \(\pi r^{2}\)
2. c. Radius