Question

the volume of a conical vase is 90 cubic centimeters, and the radius of its base is 4 centimeters. calculate the height of the vase. use 3.14 for π. round your answer to the nearest tenth.
use the keypad to type your answer in the box provided.
the height of the vase is centimeters.

Explanation:

Step1: Write the formula for the volume of a cone

The volume formula of a cone is \( V=\frac{1}{3}\pi r^{2}h\), where \(V\) is the volume, \(r\) is the radius of the base, and \(h\) is the height.

Step2: Rearrange the formula to solve for \(h\)

From \( V = \frac{1}{3}\pi r^{2}h\), we can get \(h=\frac{3V}{\pi r^{2}}\).

Step3: Substitute the given values into the formula

Given \(V = 90\space cm^{3}\), \(r = 4\space cm\), and \(\pi=3.14\).
Substitute these values into \(h=\frac{3V}{\pi r^{2}}\):
\(h=\frac{3\times90}{3.14\times4^{2}}\)
First, calculate \(3\times90 = 270\) and \(4^{2}=16\), then \(3.14\times16 = 50.24\).
So \(h=\frac{270}{50.24}\)
\(h\approx5.4\)

Answer:

\(5.4\)