Question

the bases of cylinder a and cylinder b are circles with the same radius. the volume of cylinder a is 100π cubic centimeters. what is the volume of cylinder b? write an exact answer in terms of π. cubic centimeters

Explanation:

Step1: Find the base area of cylinder A

The volume formula of a cylinder is \(V = S\times h\) (where \(V\) is volume, \(S\) is base - area, \(h\) is height). For cylinder A, \(V_A=100\pi\space cm^3\) and \(h_A = 4\space cm\). Then \(S=\frac{V_A}{h_A}\).

$$S=\frac{100\pi}{4}=25\pi\space cm^2$$

Step2: Calculate the volume of cylinder B

Cylinder B is an oblique cylinder. The volume formula of an oblique cylinder is also \(V = S\times h\) (where \(h\) is the perpendicular height). Since the two cylinders have the same base - radius, their base - areas are equal (\(S = 25\pi\space cm^2\)), and the perpendicular height of cylinder B \(h_B=4\space cm\).

$$V_B=S\times h_B$$

Substitute \(S = 25\pi\) and \(h_B = 4\) into the formula:

$$V_B=25\pi\times4 = 100\pi\space cm^3$$

Answer:

\(100\pi\)