Question

the height of a cylinder is 7 inches. another cylinder with the same size base has double the volume. what is the height of the second cylinder? 14 in. 28 in. 7 in. 3.5 in.

Explanation:

Step1: Recall the volume formula of a cylinder

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

Step2: Analyze the relationship between the two cylinders

Let the radius of the base of both cylinders be \(r\). For the first cylinder, \(V_1=\pi r^{2}h_1\) with \(h_1 = 7\) inches. For the second cylinder, \(V_2=\pi r^{2}h_2\), and \(V_2 = 2V_1\).
Substitute \(V_1\) and \(V_2\) into the equation: \(\pi r^{2}h_2=2\times\pi r^{2}h_1\).
Since \(r
eq0\) (because if \(r = 0\), there is no - real - cylinder), we can divide both sides of the equation \(\pi r^{2}h_2 = 2\pi r^{2}h_1\) by \(\pi r^{2}\).
We get \(h_2=2h_1\).

Step3: Calculate the height of the second cylinder

Substitute \(h_1 = 7\) inches into \(h_2 = 2h_1\). Then \(h_2=2\times7=14\) inches.

Answer:

14 in.